$course$/top/Default for MSII/Test #12 $course$/top/Default for MSII/Test #12/L89- Similar and Congruent Triangles L73- Intersecting Lines {v1a}{v1b} and {v2a}{v2b} intersect at point {v0}. {angleInfo} var board = JXG.JSXGraph.initBoard(BOARDID,{ axis:false, grid:false, boundingbox: [-2,2,2,-2], showCopyright: false, showNavigation: false, keepAspectRatio: true}); var p1a=board.create('point',[{Xa},{Ya}],{ name:"{v1a}", size:"1", fixed:true, showInfobox:false}); var p1b=board.create('point',[-{Xa},-{Ya}],{ name:"{v1b}", size:"1", fixed:true, showInfobox:false}); var p0=board.create('point',[0,0],{name:"{v0}",size:"1",fixed:true,showInfobox:false}); var line1=board.create('line',[p1a,p1b],{firstArrow:true,lastArrow:true,}); var p2a=board.create('point',[{Xb},{Yb}],{name:"{v2a}",size:"1",fixed:true,showInfobox:false}); var p2b=board.create('point',[-1*{Xb},-1*{Yb}],{name:"{v2b}",size:"1", fixed:true, showInfobox:false}); var line2=board.create('line',[p0,p2a],{firstArrow:true,lastArrow:true,}); var t1=board.create('text',[.25,0,"{disRight}"],{anchorX:'left',anchorY:'middle',fontSize:20}); var t1=board.create('text',[0,.25,"{disUpper}"],{anchorX:'middle',anchorY:'middle',fontSize:20}); ]]> 3.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. ooo"),join("","Angle ",v1a,v0,v2a," = ",upper,"^o")); partI=pick(given,join("","Angle ",v1a,v0,v2a),join("","Angle ",v1a,v0,v2b)); partIAns=pick(given,upper,right); partIFB=pick(given,join("","Angle ",v1a,v0,v2a," = ",upper,"^o.
180^o - ",right,"^o = ",upper,"^o"),join("","Angle ",v1a,v0,v2b," = ",right,".
180^o - ",upper,"^o = ",right,"^o")); partII=pick(randPart,join("","Angle ",v1b,v0,v2a),join("","Angle ",v1b,v0,v2b)); partIIAns=pick(randPart,right,upper); partIIFB=pick(randPart,join("","Angle ",v1b,v0,v2a," = Angle ",v1a,v0,v2b,"
Angle ",v1b,v0,v2a," = ",right,"^o"),join("","Angle ",v1b,v0,v2b," = Angle ",v1a,v0,v2a,"
Angle ",v1b,v0,v2b," = ",upper,"^o")); choices=[join("",v1b,v0,v2b),join("",v1b,v0,v2a),join("",v1a,v0,v2b),join("",v1a,v0,v2a)]; angCong=pick(randAngle,3,2,1,0); ang1=pick(randAngle,join("",v1b,v0,v2b),join("",v1b,v0,v2a),join("",v1a,v0,v2b),join("",v1a,v0,v2a));]]> abc 0 1 0 1 partIAns _err == 0 1 1 {partI}= {_0}^o

]]> {partIFB}

]]> 1 1 0 1 partIIAns _err == 0 1 1 {partII}= {_0}^o

]]> {partIIFB}

]]> 2 1 0 1 angCong _err == 0 1 1 An angle is always congruent to itself. Name a second angle that is congruent to <{ang1} (do not choose <{ang1}.)

< {ang1} ≡ {_0:choices:MCE}

]]> var board = JXG.JSXGraph.initBoard(BOARDID,{ axis:false, grid:false, boundingbox: [-2,2,2,-2], showCopyright: false, showNavigation: false, keepAspectRatio: true}); var p1a=board.create('point',[{Xa},{Ya}],{ name:"{v1a}", size:"1", fixed:true, showInfobox:false}); var p1b=board.create('point',[-{Xa},-{Ya}],{ name:"{v1b}", size:"1", fixed:true, showInfobox:false}); var p0=board.create('point',[0,0],{name:"{v0}",size:"1",fixed:true,showInfobox:false}); var line1=board.create('line',[p1a,p1b],{firstArrow:true,lastArrow:true,}); var p2a=board.create('point',[{Xb},{Yb}],{name:"{v2a}",size:"1",fixed:true,showInfobox:false}); var p2b=board.create('point',[-1*{Xb},-1*{Yb}],{name:"{v2b}",size:"1", fixed:true, showInfobox:false}); var line2=board.create('line',[p0,p2a],{firstArrow:true,lastArrow:true,}); var t1=board.create('text',[.25,0,"{right}"],{anchorX:'left',anchorY:'middle',fontSize:20,strokeColor:'red'}); var t2=board.create('text',[0,.25,"{upper}"],{anchorX:'middle',anchorY:'middle',fontSize:20,strokeColor:'green'}); var t3=board.create('text',[-.25,0,"{right}"],{anchorX:'right',anchorY:'middle',fontSize:20,strokeColor:'red'}); var t4=board.create('text',[0,-.25,"{upper}"],{anchorX:'middle',anchorY:'middle',fontSize:20,strokeColor:'green'}); {=choices[0]} ≡ <{=choices[3]} and <{=choices[1]} ≡ <{=choices[2]}]]> L89-Congruent Triangles (bow-similar) var board=JXG.JSXGraph.initBoard(BOARDID,{ boundingbox:[-1.5,1.5,1.5,-1.5], axis:false, grid:false, showCopyright:false, showNavigation:false, keepaspectratio:true }); var pA=board.create('point',[{Xa},{Ya}],{fixed:true,size:'0',name:'',showInfoBox:false}); var tA=board.create('text',[{Xa},{Ya}-.1,"{At}"]); var pB=board.create('point',[{Xb},{Yb}],{fixed:true,size:'0',name:'',showInfoBox:false}); var tB=board.create('text',[{Xb},{Yb}+.1,"{Bt}"]); var pC=board.create('point',[{Xc},{Yc}],{fixed:true,size:'0',name:'',showInfoBox:false}); var tC=board.create('text',[{Xc},{Yc}+.1,"{Ct}"]); var Tri1= board.create('polygon',[pA,pB,pC],{fillColor:'{color1}',strokeColor:'{color1}'}); var pD=board.create('point',[{Xd},{Yd}],{fixed:true,size:'0',name:'',showInfoBox:false}); var tB=board.create('text',[{Xd},{Yd}+.1,"{Dt}"]); var pE=board.create('point',[{Xe},{Ye}],{fixed:true,size:'0',name:'',showInfoBox:false}); var tB=board.create('text',[{Xe},{Ye}-.1,"{Et}"]); var pF=board.create('point',[{Xf},{Yf}],{fixed:true,size:'0',name:'',showInfoBox:false}); var Tri1= board.create('polygon',[pD,pE,pF],{fillColor:'{color2}',strokeColor:'{color2}'}); ]]> 2.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. none 0 1 0 1 ans randChoice[_0]==ans 1 1 The triangles are {_0:displayChoice}]]> The triangles are {relationship}.

]]> 1 1 0 4 [ans,ans,wAns,wAns] (randSides[_0]==ans*.25) + (randSides[_1]==ans*.25) + (randSides[_2]==wAns*.25) + (randAngles[_3]==wAns*.25) 1 1

Triangle are congruent if their corresponding sides are {_0:displaySides:MCE}, and their corresponding angles are {_1:displayAngles:MCE}.

Triangle are similar if their corresponding sides are {_2:displaySides:MCE}, and their corresponding angles are {_3:displayAngles:MCE}.

]]>

Triangle are congruent if their corresponding sides are congruent, and their corresponding angles are congruent.

Triangle are similar if their corresponding sides are proportional, and their corresponding angles are congruent.

]]> TL73- Congruent Angles var board = JXG.JSXGraph.initBoard(BOARDID,{ axis:false,grid:false, boundingbox: [-1.5,1.5,4,-1.5], showCopyright: false, showNavigation: false }); var p1=board.create('point',[{Xa},{Ya}],{name:"{Aname}",size:"1",showInfobox:false,fixed:true}); var p2=board.create('point',[0,0],{name:"",size:"1",showInfobox:false,fixed:true}); var p3=board.create('point',[1,0],{name:"{Cname}",size:"1",showInfobox:false,fixed:true}); var r1=board.create('line',[p2,p1],{strokeColor:'black',straightFirst:false,straightLast:false,arrowLast:true}); var r2=board.create('line',[p2,p3],{strokeColor:'black',straightFirst:false,straightLast:false,arrowLast:true}); var t1=board.create('text',[{Xa}/2,.1,"{angDeg} ^o"],{anchorX:'left',anchorY:'middle',fixed:true,fontSize:'10'}); var t2=board.create('text',[0,-0.1,"{Bname}"],{anchorX:'middle',anchorY:'middle',fixed:true,fontSize:'10'}); var p3=board.create('point',[{Xb}+2.5,{Yb}],{name:"{Dname}",size:"1",showInfobox:false,fixed:true}); var p0=board.create('point',[2.5,0],{name:"{Ename}",size:"1",showInfobox:false,fixed:true}); var p4=board.create('point',[{Xc}+2.5,{Yc}],{name:"{Fname}",size:"1",showInfobox:false,fixed:true}); var r3=board.create('line',[p0,p3],{strokeColor:'black',straightFirst:false,straightLast:false,arrowLast:true}); var r4=board.create('line',[p0,p4],{strokeColor:'black',straightFirst:false,straightLast:false,arrowLast:true}); ]]> Congruent means equal in measure.

Angle {Aname}{Bname}{Cname} is congruent to angle {Dname}{Ename}{Fname}.

Angle {Dname}{Ename}{Fname} = {angDeg}^o.

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. angDeg=round(ang*180/pi(),0); Xa=cos(ang); Ya=sin(ang); Xb= cos(offset); Yb=sin(offset); Xc=cos(offset+ang); Yc=sin(offset+ang); Aname=segNames[0]; Bname=segNames[1]; Cname=segNames[2]; Dname=segNames[3]; Ename=segNames[4]; Fname=segNames[5]; abc 0 1 0 1 angDeg _err == 0 1 1 < {Dname}{Ename}{Fname}= {_0}^o

]]> TL73- Congruent Line Segments var board = JXG.JSXGraph.initBoard(BOARDID,{ axis:false,grid:false, boundingbox: [-1,1.5,5,0], showCopyright: false, showNavigation: false }); var p1=board.create('point',[0,1],{name:"{Aname}",size:"1",showInfobox:false,fixed:true}); var p2=board.create('point',[4,1],{name:"{Bname}",size:"1",showInfobox:false,fixed:true}); var l1=board.create('line',[p1,p2],{strokeColor:'black',straightFirst:false,straightLast:false}); var t1=board.create('text',[2,1,"{segLength} {unit}"],{anchorX:'middle',anchorY:'top',fixed:true,fontSize:'20'}); var p3=board.create('point',[0,.5],{name:"{Cname}",size:"1",showInfobox:false,fixed:true}); var p4=board.create('point',[4,.5],{name:"{Dname}",size:"1",showInfobox:false,fixed:true}); var l2=board.create('line',[p3,p4],{strokeColor:'black',straightFirst:false,straightLast:false}); var t2=board.create('text',[2,.5,"x {unit}"],{anchorX:'middle',anchorY:'top',fixed:true,fontSize:'20'}); ]]> Congruent means equal in measure.

{Cname}{Dname} is equal in length to line segment {Aname}{Bname}, therefore it is {segLength} {unit}.

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. Aname=segNames[0]; Bname=segNames[1]; Cname=segNames[2]; Dname=segNames[3]; abc 0 1 0 1 segLength _err == 0 1 1 {Cname}{Dname}= {_0} {unit}

]]> TL73-Congruent Triangles var board=JXG.JSXGraph.initBoard(BOARDID,{ boundingbox:[-1.25,1.25,1.25,-1.25], axis:false, grid:false, showCopyright:false, showNavigation:false, keepaspectratio:true }); var pA=board.create('point',[{Xa},{Ya}],{fixed:true,size:'0',name:'',showInfoBox:false}); var tA=board.create('text',[{Xa},{Ya},"A"],{fixed:true,fontSize:15}); var pB=board.create('point',[{Xb},{Yb}],{fixed:true,size:'0',name:'',showInfoBox:false}); var tB=board.create('text',[{Xb},{Yb},"B"],{fixed:true,fontSize:15,anchorY:'middle',anchorX:'right'}); var pC=board.create('point',[{Xc},{Yc}],{fixed:true,size:'0',name:'',showInfoBox:false}); var tC=board.create('text',[{Xc},{Yc},"C"],{fixed:true,fontSize:15,anchorX:'middle',anchorY:'top'}); var Tri1= board.create('polygon',[pA,pB,pC],{fillColor:'{color1}',strokeColor:'{color1}'}); var board1=JXG.JSXGraph.initBoard(BOARDID,{ boundingbox:[-1.25,1.25,1.25,-1.25], axis:false, grid:false, showCopyright:false, showNavigation:false, keepaspectratio:true }); var pD=board1.create('point',[{Xd},{Yd}],{fixed:true,size:'0',name:'',showInfoBox:false}); var tD=board1.create('text',[{Xd},{Yd},"D"],{fixed:true,fontSize:15}); var pE=board1.create('point',[{Xe},{Ye}],{fixed:true,size:'0',name:'',showInfoBox:false}); var tE=board1.create('text',[{Xe},{Ye},"E"],{fixed:true,fontSize:15,anchorY:'middle',anchorX:'right'}); var pF=board1.create('point',[{Xf},{Yf}],{fixed:true,size:'0',name:'',showInfoBox:false}); var reflect={transReflect}; if (reflect==1) { var tF=board1.create('text',[{Xf},{Yf},"F"],{fixed:true,fontSize:15,anchorY:'bottom',anchorX:'right'}); } else { var tF=board1.create('text',[{Xf},{Yf},"F"],{fixed:true,fontSize:15,anchorY:'top',anchorX:'right'}); } var Tri1= board1.create('polygon',[pD,pE,pF],{fillColor:'{color2}',strokeColor:'{color2}'}); ]]> 2.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. none 0 1 0 1 ans randChoice[_0]==ans 1 1 The triangles are {_0:displayChoice}]]> The triangles are {relationship}.

]]> 1 1 0 4 [ans,ans,wAns,wAns] (randSides[_0]==ans*.25) + (randSides[_1]==ans*.25) + (randSides[_2]==wAns*.25) + (randAngles[_3]==wAns*.25) 1 1

Triangle are congruent if their corresponding sides are {_0:displaySides:MCE}, and their corresponding angles are {_1:displayAngles:MCE}.

Triangle are similar if their corresponding sides are {_2:displaySides:MCE}, and their corresponding angles are {_3:displayAngles:MCE}.

]]>

Triangle are congruent if their corresponding sides are congruent, and their corresponding angles are congruent.

Triangle are similar if their corresponding sides are proportional, and their corresponding angles are congruent.

]]> TL73-Congruent Triangles (bow) var board=JXG.JSXGraph.initBoard(BOARDID,{ boundingbox:[-1.5,1.5,1.5,-1.5], axis:false, grid:false, showCopyright:false, showNavigation:false, keepaspectratio:true }); var pA=board.create('point',[{Xa},{Ya}],{fixed:true,size:'0',name:'',showInfoBox:false}); var tA=board.create('text',[{Xa},{Ya}-.1,"{At}"]); var pB=board.create('point',[{Xb},{Yb}],{fixed:true,size:'0',name:'',showInfoBox:false}); var tB=board.create('text',[{Xb},{Yb}+.1,"{Bt}"]); var pC=board.create('point',[{Xc},{Yc}],{fixed:true,size:'0',name:'',showInfoBox:false}); var tC=board.create('text',[{Xc},{Yc}+.1,"{Ct}"]); var Tri1= board.create('polygon',[pA,pB,pC],{fillColor:'{color1}',strokeColor:'{color1}'}); var pD=board.create('point',[{Xd},{Yd}],{fixed:true,size:'0',name:'',showInfoBox:false}); var tB=board.create('text',[{Xd},{Yd}+.1,"{Dt}"]); var pE=board.create('point',[{Xe},{Ye}],{fixed:true,size:'0',name:'',showInfoBox:false}); var tB=board.create('text',[{Xe},{Ye}-.1,"{Et}"]); var pF=board.create('point',[{Xf},{Yf}],{fixed:true,size:'0',name:'',showInfoBox:false}); var Tri1= board.create('polygon',[pD,pE,pF],{fillColor:'{color2}',strokeColor:'{color2}'}); ]]> 2.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. none 0 1 0 1 ans randChoice[_0]==ans 1 1 The triangles are {_0:displayChoice}]]> The triangles are {relationship}.

]]> 1 1 0 4 [ans,ans,wAns,wAns] (randSides[_0]==ans*.25) + (randSides[_1]==ans*.25) + (randSides[_2]==wAns*.25) + (randAngles[_3]==wAns*.25) 1 1

Triangle are congruent if their corresponding sides are {_0:displaySides:MCE}, and their corresponding angles are {_1:displayAngles:MCE}.

Triangle are similar if their corresponding sides are {_2:displaySides:MCE}, and their corresponding angles are {_3:displayAngles:MCE}.

]]>

Triangle are congruent if their corresponding sides are congruent, and their corresponding angles are congruent.

Triangle are similar if their corresponding sides are proportional, and their corresponding angles are congruent.

]]> TL73-Congruent Triangles (copy) var board=JXG.JSXGraph.initBoard(BOARDID,{ boundingbox:[-1.25,1.25,1.25,-1.25], axis:false, grid:false, showCopyright:false, showNavigation:false, keepaspectratio:true }); var pA=board.create('point',[{Xa},{Ya}],{fixed:true,size:'0',name:'',showInfoBox:false}); var tA=board.create('text',[{Xa},{Ya},"A"],{fixed:true,fontSize:15}); var pB=board.create('point',[{Xb},{Yb}],{fixed:true,size:'0',name:'',showInfoBox:false}); var tB=board.create('text',[{Xb},{Yb},"B"],{fixed:true,fontSize:15,anchorY:'middle',anchorX:'right'}); var pC=board.create('point',[{Xc},{Yc}],{fixed:true,size:'0',name:'',showInfoBox:false}); var tC=board.create('text',[{Xc},{Yc},"C"],{fixed:true,fontSize:15,anchorX:'middle',anchorY:'top'}); var Tri1= board.create('polygon',[pA,pB,pC],{fillColor:'{color1}',strokeColor:'{color1}'}); var board1=JXG.JSXGraph.initBoard(BOARDID,{ boundingbox:[-2.5,2.5,2.5,-2.5], axis:false, grid:false, showCopyright:false, showNavigation:false, keepaspectratio:true }); var pD=board1.create('point',[{Xd},{Yd}],{fixed:true,size:'0',name:'',showInfoBox:false}); var tD=board1.create('text',[{Xd},{Yd},"D"],{fixed:true,fontSize:15}); var pE=board1.create('point',[{Xe},{Ye}],{fixed:true,size:'0',name:'',showInfoBox:false}); var tE=board1.create('text',[{Xe},{Ye},"E"],{fixed:true,fontSize:15,anchorY:'middle',anchorX:'right'}); var pF=board1.create('point',[{Xf},{Yf}],{fixed:true,size:'0',name:'',showInfoBox:false}); var reflect={transReflect}; if (reflect==1) { var tF=board1.create('text',[{Xf},{Yf},"F"],{fixed:true,fontSize:15,anchorY:'bottom',anchorX:'right'}); } else { var tF=board1.create('text',[{Xf},{Yf},"F"],{fixed:true,fontSize:15,anchorY:'top',anchorX:'right'}); } var Tri1= board1.create('polygon',[pD,pE,pF],{fillColor:'{color2}',strokeColor:'{color2}'}); ]]> 2.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. none 0 1 0 1 ans randChoice[_0]==ans 1 1 The triangles are {_0:displayChoice}]]> The triangles are {relationship}.

]]> 1 1 0 4 [ans,ans,wAns,wAns] (randSides[_0]==ans*.25) + (randSides[_1]==ans*.25) + (randSides[_2]==wAns*.25) + (randAngles[_3]==wAns*.25) 1 1

Triangle are congruent if their corresponding sides are {_0:displaySides:MCE}, and their corresponding angles are {_1:displayAngles:MCE}.

Triangle are similar if their corresponding sides are {_2:displaySides:MCE}, and their corresponding angles are {_3:displayAngles:MCE}.

]]>

Triangle are congruent if their corresponding sides are congruent, and their corresponding angles are congruent.

Triangle are similar if their corresponding sides are proportional, and their corresponding angles are congruent.

]]> TL73-Congruent Triangles (corresponding angles) var board=JXG.JSXGraph.initBoard(BOARDID,{ boundingbox:[-4,4,4,-4], axis:false, grid:false, showCopyright:false, showNavigation:false, keepaspectratio:true }); var pA=board.create('point',[{Xa},{Ya}],{fixed:true,size:'0', name:'{A}', showInfoBox:false}); var pB=board.create('point',[{Xb},{Yb}],{fixed:true, size:'0',name:'{B}', showInfoBox:false}); var pC=board.create('point',[{Xc},{Yc}],{fixed:true,size:'0',name:'{C}', showInfoBox:false,vertices:{offset:[-1,-1]}}); var Tri1= board.create('polygon',[pA,pB,pC],{fillColor:'{color1}',strokeColor:'{color1}'}); var pD=board.create('point',[{Xd},{Yd}],{fixed:true,size:'0',name:'{D}', showInfoBox:false}); var pE=board.create('point',[{Xe},{Ye}],{fixed:true,size:'0',name:'{E}', showInfoBox:false}); var pF=board.create('point',[{Xf},{Yf}],{fixed:true,size:'0',name:'{F}', showInfoBox:false}); var Tri1= board.create('polygon',[pD,pE,pF],{fillColor:'{color2}',strokeColor:'{color2}'}); ]]> Δ{=abcArray[0]}{=abcArray[1]}{=abcArray[2]} ≡ Δ{=defArray[0]}{=defArray[1]}{=defArray[2]}

The triangles are {relationship}.

{=abcArray[0]} ≡ {=defArray[0]}

{=abcArray[1]} ≡ {=defArray[1]}

{=abcArray[2]} ≡ {=defArray[2]}

]]> 3.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. none 0 1 0 1 0 orderA[0] == orderD[_0] 1 1 {=ABCChoices[0]} ≡ {_0:DEFChoices:MCE} 1 1 0 1 1 orderA[1] == orderD[_0] 1 1 2 1 0 1 2 orderA[2] == orderD[_0] 1 1 TL73-Congruent Triangles (corresponding sides) var board=JXG.JSXGraph.initBoard(BOARDID,{ boundingbox:[-4,4,4,-4], axis:false, grid:false, showCopyright:false, showNavigation:false, keepaspectratio:true }); var pA=board.create('point',[{Xa},{Ya}],{fixed:true,size:'0', name:'{A}', showInfoBox:false}); var pB=board.create('point',[{Xb},{Yb}],{fixed:true, size:'0',name:'{B}', showInfoBox:false}); var pC=board.create('point',[{Xc},{Yc}],{fixed:true,size:'0',name:'{C}', showInfoBox:false,vertices:{offset:[-1,-1]}}); var Tri1= board.create('polygon',[pA,pB,pC],{fillColor:'{color1}',strokeColor:'{color1}'}); var pD=board.create('point',[{Xd},{Yd}],{fixed:true,size:'0',name:'{D}', showInfoBox:false}); var pE=board.create('point',[{Xe},{Ye}],{fixed:true,size:'0',name:'{E}', showInfoBox:false}); var pF=board.create('point',[{Xf},{Yf}],{fixed:true,size:'0',name:'{F}', showInfoBox:false}); var Tri1= board.create('polygon',[pD,pE,pF],{fillColor:'{color2}',strokeColor:'{color2}'}); ]]> Δ{=vertices[0]}{=vertices[1]}{=vertices[2]} ≡ Δ{=vertices[3]}{=vertices[4]}{=vertices[5]}

The triangles are {relationship}.

{=abcArray[0]} ≡ {=defArray[0]}

{=abcArray[1]} ≡ {=defArray[1]}

{=abcArray[2]} ≡ {=defArray[2]}

]]> 3.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. none 0 1 0 1 0 orderA[0] == orderD[_0] 1 1 {=ABCChoices[0]} ≡ {_0:DEFChoices:MCE} 1 1 0 1 1 orderA[1] == orderD[_0] 1 1 2 1 0 1 2 orderA[2] == orderD[_0] 1 1 TL73-Similar Triangles var board=JXG.JSXGraph.initBoard(BOARDID,{ boundingbox:[-4,4,4,-4], axis:false, grid:false, showCopyright:false, showNavigation:false, keepaspectratio:true }); var pA=board.create('point',[{Xa},{Ya}],{fixed:true,size:'0',name:'A',showInfoBox:false}); var pB=board.create('point',[{Xb},{Yb}],{fixed:true,size:'0',name:'B',showInfoBox:false}); var pC=board.create('point',[{Xc},{Yc}],{fixed:true,size:'0',name:'C',showInfoBox:false}); var Tri1= board.create('polygon',[pA,pB,pC],{fillColor:'{color1}',strokeColor:'{color1}'}); var pD=board.create('point',[{Xd},{Yd}],{fixed:true,size:'0',name:'D',showInfoBox:false}); var pE=board.create('point',[{Xe},{Ye}],{fixed:true,size:'0',name:'E',showInfoBox:false}); var pF=board.create('point',[{Xf},{Yf}],{fixed:true,size:'0',name:'F',showInfoBox:false}); var Tri1= board.create('polygon',[pD,pE,pF],{fillColor:'{color2}',strokeColor:'{color2}'}); ]]> 2.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. none 0 1 0 1 ans randChoice[_0]==ans 1 1 The triangles are {_0:displayChoice}]]> The triangles are {relationship}.

]]> 1 1 0 4 [ans,ans,wAns,wAns] (randSides[_0]==ans*.25) + (randSides[_1]==ans*.25) + (randSides[_2]==wAns*.25) + (randAngles[_3]==wAns*.25) 1 1 Triangle are congruent if their corresponding sides are {_0:displaySides:MCE}, and their corresponding angles are {_1:displayAngles:MCE}.

Triangle are similar if their corresponding sides are {_2:displaySides:MCE}, and their corresponding angles are {_3:displayAngles:MCE}.

]]>

Triangle are congruent if their corresponding sides are congruent, and their corresponding angles are congruent.

Triangle are similar if their corresponding sides are proportional, and their corresponding angles are congruent.

]]> TL73-Similar Triangles-2 boards var board=JXG.JSXGraph.initBoard(BOARDID,{ boundingbox:[-2.25,2.25,2.25,-2.25], axis:false, grid:false, showCopyright:false, showNavigation:false, keepaspectratio:true }); var pA=board.create('point',[{Xa},{Ya}],{fixed:true,size:'0',name:'',showInfoBox:false}); var tA=board.create('text',[{Xa},{Ya},"A"],{fixed:true,fontSize:15}); var pB=board.create('point',[{Xb},{Yb}],{fixed:true,size:'0',name:'',showInfoBox:false}); var tB=board.create('text',[{Xb},{Yb},"B"],{fixed:true,fontSize:15,anchorY:'middle',anchorX:'right'}); var pC=board.create('point',[{Xc},{Yc}],{fixed:true,size:'0',name:'',showInfoBox:false}); var tC=board.create('text',[{Xc},{Yc},"C"],{fixed:true,fontSize:15,anchorX:'middle',anchorY:'top'}); var Tri1= board.create('polygon',[pA,pB,pC],{fillColor:'{color1}',strokeColor:'{color1}'}); var board1=JXG.JSXGraph.initBoard(BOARDID,{ boundingbox:[-1.25,1.25,1.25,-1.25], axis:false, grid:false, showCopyright:false, showNavigation:false, keepaspectratio:true }); var pD=board1.create('point',[{Xd},{Yd}],{fixed:true,size:'0',name:'',showInfoBox:false}); var tD=board1.create('text',[{Xd},{Yd},"D"],{fixed:true,fontSize:15}); var pE=board1.create('point',[{Xe},{Ye}],{fixed:true,size:'0',name:'',showInfoBox:false}); var tE=board1.create('text',[{Xe},{Ye},"E"],{fixed:true,fontSize:15,anchorY:'middle',anchorX:'right'}); var pF=board1.create('point',[{Xf},{Yf}],{fixed:true,size:'0',name:'',showInfoBox:false}); var reflect={transReflect}; if (reflect==1) { var tF=board1.create('text',[{Xf},{Yf},"F"],{fixed:true,fontSize:15,anchorY:'bottom',anchorX:'right'}); } else { var tF=board1.create('text',[{Xf},{Yf},"F"],{fixed:true,fontSize:15,anchorY:'top',anchorX:'right'}); } var Tri1= board1.create('polygon',[pD,pE,pF],{fillColor:'{color2}',strokeColor:'{color2}'}); ]]> 2.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. none 0 1 0 1 sim randChoice[_0]==sim 1 1 The triangles are {_0:displayChoice}]]> The triangles are {relationship}.

]]> 1 1 0 4 [ans,ans,wAns,wAns] (randSides[_0]==ans*.25) + (randSides[_1]==ans*.25) + (randSides[_2]==wAns*.25) + (randAngles[_3]==wAns*.25) 1 1

Triangle are congruent if their corresponding sides are {_0:displaySides:MCE}, and their corresponding angles are {_1:displayAngles:MCE}.

Triangle are similar if their corresponding sides are {_2:displaySides:MCE}, and their corresponding angles are {_3:displayAngles:MCE}.

]]>

Triangle are congruent if their corresponding sides are congruent, and their corresponding angles are congruent.

Triangle are similar if their corresponding sides are proportional, and their corresponding angles are congruent.

]]> $course$/top/Default for MSII/Test #12/L90-Multiplying Monomials by Binomials L83-Multiplying Monomial times binomial Simplify: {num1}{var1}^{exp1} ( {num2}{var1}^{exp2} + {num3}{var1}^{exp3} )

]]> Expand, then multiply.

{num1}{var1}^{exp1} ( {num2}{var1}^{exp2} + {num3}{var1}^{exp3} )		Given
{num1}{factor1} ( {num2}{factor2} + {num3}{factor3} )		Write the expression as a product of factors
({num1}{factor1}) ( {num2}{factor2}) + ({num1}{factor1})({num3}{factor3} )		Multiply the monomial by each term of the binomial
{=num1num2}{var1}^{exp12}+ {=num1num3}{var1}^{exp13}		The base {var1} is multiplied {exp12} times The base {var1} is multiplied {exp13} times

Distribute the monomial to each term of the binomial in parentheses

{num1}{var1}^{exp1}({num2}{var1}^{exp2} + {num3}{var1}^{exp3} )		Given
{num1}{var1}^{exp1}({num2}{var1}^{exp2}) + {num1}{var1}^{exp1}({num3}{var1}^{exp3} )		Distribute {num1}{var1}^{exp1} to each term inside the parentheses
{=num1num2}{var1}^{exp12} + {=num1num3}{var1}^{exp13}		Multiply ({num1})({num2})={=num1num2}, Add the exponents {exp1} + {exp2} = {=exp1+exp2} Multiply ({num1})({num3})={=num1num3}, Add the exponents {exp1} + {exp3} = {=exp1+exp3}
		The terms are not like terms because the exponents are different.

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. abc 0 1 0 4 [ansNum1,ans1,ansNum2,ans2] _err == 0 1 1 {_0}{var1}^{_1}+{_2}{var1}^{_3}

]]> L90-Multiplying Monomial (with exp 1) times binomial Simplify: {num1}{var1} ( {num2}{var1}^{exp2} + {num3}{var1}^{exp3} )

]]> Expand, then multiply.

{num1}{var1} ( {num2}{var1}^{exp2} + {num3}{var1}^{exp3} )		Given
{num1}{factor1} ( {num2}{factor2} + {num3}{factor3} )		Write the expression as a product of factors
({num1}{factor1}) ( {num2}{factor2}) + ({num1}{factor1})({num3}{factor3} )		Multiply the monomial by each term of the binomial
{=num1num2}{var1}^{exp12}+ {=num1num3}{var1}^{exp13}		The base {var1} is multiplied {exp12} times The base {var1} is multiplied {exp13} times

Distribute the monomial to each term of the binomial in parentheses

{num1}{var1}({num2}{var1}^{exp2} + {num3}{var1}^{exp3} )		Given {num1}{var1} = {num1}{var1}^{exp1}
{num1}{var1}^{exp1}({num2}{var1}^{exp2}) + {num1}{var1}^{exp1}({num3}{var1}^{exp3} )		Distribute {num1}{var1}^{exp1} to each term inside the parentheses
{=num1num2}{var1}^{exp12} + {=num1num3}{var1}^{exp13}		Multiply ({num1})({num2})={=num1num2}, Add the exponents {exp1} + {exp2} = {=exp1+exp2} Multiply ({num1})({num3})={=num1num3}, Add the exponents {exp1} + {exp3} = {=exp1+exp3}
		The terms are not like terms because the exponents are different.

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. abc 0 1 0 4 [ansNum1,ans1,ansNum2,ans2] _err == 0 1 1 {_0}{var1}^{_1}+{_2}{var1}^{_3}

]]> L90-Multiplying Monomial times binomial Simplify: {num1}{var1}^{exp1} ( {num2}{var1}^{exp2} + {num3}{var1}^{exp3} )

]]> Expand, then multiply.

{num1}{var1}^{exp1} ( {num2}{var1}^{exp2} + {num3}{var1}^{exp3} )		Given
{num1}{factor1} ( {num2}{factor2} + {num3}{factor3} )		Write the expression as a product of factors
({num1}{factor1}) ( {num2}{factor2}) + ({num1}{factor1})({num3}{factor3} )		Multiply the monomial by each term of the binomial
{=num1num2}{var1}^{exp12}+ {=num1num3}{var1}^{exp13}		The base {var1} is multiplied {exp12} times The base {var1} is multiplied {exp13} times

Distribute the monomial to each term of the binomial in parentheses

{num1}{var1}^{exp1}({num2}{var1}^{exp2} + {num3}{var1}^{exp3} )		Given
{num1}{var1}^{exp1}({num2}{var1}^{exp2}) + {num1}{var1}^{exp1}({num3}{var1}^{exp3} )		Distribute {num1}{var1}^{exp1} to each term inside the parentheses
{=num1num2}{var1}^{exp12} + {=num1num3}{var1}^{exp13}		Multiply ({num1})({num2})={=num1num2}, Add the exponents {exp1} + {exp2} = {=exp1+exp2} Multiply ({num1})({num3})={=num1num3}, Add the exponents {exp1} + {exp3} = {=exp1+exp3}
		The terms are not like terms because the exponents are different.

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. abc 0 1 0 4 [ansNum1,ans1,ansNum2,ans2] _err == 0 1 1 {_0}{var1}^{_1}+{_2}{var1}^{_3}

]]> $course$/top/Default for MSII/Test #12/L85-Percent-Sales Tax and Discounts L85-Discount A {name} costs ${price}. It is on sale for {percent}% off, how much is the discount? {name} costs ${price}
Discount: {percent}%
Given

{percent}% = {decimalR}
1. Change the percent discount to a decimal number.

Discount amount = ({decimalR})({price})=${discount}
2. Multiply the percent (in decimal form) by the item price

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. randFactor={1,2,3,4,5,6,7,8,9,10}; randItem={0,1,2,3,4,5}; percent={10,15,20,25,30,35,50,60}; abc 0 1 0 1 discount _err == 0 1 1 The discount for {name} is ${_0}.

]]> L85-Discount (decimal amounts) A {name} costs ${price}. It is on sale for {percent}% off, how much is the discount? {name} costs ${price}
Discount: {percent}%
Given

{percent}% = {decimalR}
1. Change the percent discount to a decimal number.

Discount amount = ({decimalR})({price})=${discount}
2. Multiply the percent (in decimal form) by the item price

Round to the nearest cent: ${=round(discount,2)} ]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. randFactor={1,2,3,4,5,6,7,8,9,10}; randItem={0,1,2,3,4,5}; percent={10,15,20,25,30,35,50,60}; dimes={1,2,3,4,5,6,7,8,9}; cents={1,2,3,4,5,6,7,8,9}; abc 0 1 0 1 round(discount,2) _err == 0 1 1 The discount to the nearest cent is ${_0}.

]]> L85-Sale item A {name} costs ${price}. How much does the {name} cost when it is on sale for {percent}% off? {name} costs ${price}
Discount: {percent}%
Given

{percent}% = {decimalR}
1. Change the percent discount to a decimal number.

Discount amount = ({decimalR})({price})=${discount}
2. Multiply the percent (in decimal form) by the item price

Sale price = {price} - {discount} = ${cost}
3. Subtract the discount amount from the item price.

Sale Price = ${costAns} 4. Round to the nearest cent. ]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. randFactor={1,2,3,4,5,6,7,8,9,10}; randItem={0,1,2,3,4,5}; percent={10,15,20,25,30,35,50,60}; abc 0 1 0 1 costAns _err == 0 1 1 The sale price for {name} is ${_0}.

]]> L85-Sale item with decimal amounts ]]> {name} costs ${price}
Discount: {percent}%
Given

{percent}% = {decimalR}
1. Change the percent discount to a decimal number.

Discount amount = ({decimalR})({price})=${discount}
2. Multiply the percent (in decimal form) by the item price

Sale price = {price} - {discount} = ${cost}
3. Subtract the discount amount from the item price.

Sale Price = ${costAns} 4. Round the answer to the nearest cent. ]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. randFactor={1,2,3,4,5,6,7,8,9,10}; randItem={0,1,2,3,4,5}; percent={10,15,20,25,30,35,50,60}; cents={.01:.99:.01}; abc 0 1 0 1 costAns 1 1 Round the answer to the nearest cent.
The sale price for {name} is ${_0}.

]]> L85-Tax Item ]]> {name} costs ${price}
Tax Rate: {percent}%
Given

{percent}% = {decimalR}
1. Change the percent discount to a decimal number.

Tax amount = ({decimalR})({price})=${discountText}
2. Multiply the percent (in decimal form) by the item price

Total price = {price} + {discountText} = ${costText}
3. Add the amount of tax from the item price.

Total Price = ${costText} 4. Round to the nearest cent. ]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. randFactor={1,2,3,4,5,6,7,8,9,10}; randItem={0,1,2,3,4,5}; percent={4:9:.1}; abc 0 1 0 1 costAns _err == 0 1 1 The total price for {name} is ${_0}.

]]> L85-Tax Item (decimal Amounts) /* actualWidth width of the input checkWidth width at which the box becomes wider defaultWidth default width of the box c, ctx see https://www.w3schools.com/tags/canvas_measuretext.asp size size of the font w/ px, e.g. '14 px' note that the size of the font can be defined in any units, e.g. small, medium, xx-large, 150%, 1.25cm, 22px since it is always transformed into px units sizeN size of the font w/o px, e.g. '14' family family of the font, eg. "Times New Roman", Times, serif txt text of the input, e.g. '123456' */ var defaultWidth = 30; document.write('

'); function newWidth() { var txt = $(".formulas_number").val(); var size = $(".formulas_number").css('font-size'); var sizeN = Number(size.substring(0, size.length - 2)); var family = $(".formulas_number").css('font-family'); var c = document.getElementById("canvas_1"); var ctx = c.getContext("2d"); ctx.font = size + " " + family; var actualWidth = ctx.measureText(txt).width; var checkWidth = defaultWidth - sizeN; if (actualWidth >= checkWidth) { $(".formulas_number").width(actualWidth + sizeN); } else { $(".formulas_number").width(defaultWidth); } } $(document).ready(function() { $(".formulas_number").css("padding-left", "10px"); newWidth(); $(".formulas_number").keyup(function() { newWidth(); }); }); ]]> {name} costs ${disPrice}
Tax Rate: {percent}%
Given

{percent}% = {decimalR}
1. Change the percent discount to a decimal number.

Tax amount = ({decimalR})({disPrice})=${discount}
2. Multiply the percent (in decimal form) by the item price

Total price = {disPrice} + {discount} = ${cost}
3. Add the amount of tax from the item price.

Total Price = ${costAns} 4. Round to the nearest cent. ]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. randFactor={1,2,3,4,5,6,7,8,9,10}; randItem={0,1,2,3,4,5}; percent={4:9:.1}; cents={.01:.99:.01}; abc 0 1 0 1 costAns _err == 0 1 1 The total price for {name} is ${_0}.

]]> $course$/top/Default for MSII/Test #12/L91- Non Standard Form - Linear Equations L84 - Graph Equation y- mx =0 (fractional slope) (y-int of 0)

Graph the linear equation y {signOm}$\frac{{DmNum}}{{DmDen}}$x =0 using the slope and y-intercept.

{#A}]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. mA={[1,2],[1,3],[2,3],[1,4],[2,4],[3,4],[1,5],[2,5],[3,5],[1,6],[2,6],[3,6],[4,6],[5,6],[1,7],[2,7],[3,7],[4,7],[5,7],[6,7],[1,8],[2,8],[3,8],[4,8],[5,8],[6,8],[7,8],[1,10],[2,10],[3,10],[4,10],[5,10],[6,10],[7,10],[8,10],[9,10],[2,1],[3,1],[3,2],[4,1],[4,2],[4,3],[5,1],[5,2],[5,3],[6,1],[6,2],[6,3],[6,4]}; b={-7:-1,1:7}; bn={1:99999}; signM={-1,1}; 0,join("","Go down ",abs(mNum)," because the slope is negative"),join("","Go up ",abs(mNum)," because the slope is positive")); signb=pick(b>=0,"-","+"); disb=abs(b); signm=pick(signM>0,"-",""); signMm=pick(signM>0,"-","+"); signOm=pick(signM>0,"+","-"); DmNum=abs(mNum); DmDen=abs(mDen); mNumPb=mNum+b;]]> none 0 #A 1 0 4 [0,b,mDen,mNum+b] ((_1==b+m*_0)*.5) + ((_3==b+m*_2)*.5) 1 1

]]> y {signOm}$\frac{{DmNum}}{{DmDen}}$x =0 Given {signMm}$\frac{{DmNum}}{{DmDen}}$x {signMm}$\frac{{DmNum}}{{DmDen}}$x Move the x term to the right side of the equation y = {signm}$\frac{{DmNum}}{{DmDen}}$x
The equation is in slope-intercept form A line can be graphed from two points.

1. Locate the y-intercept. This is the first point.

Since 0 can be added to the equation without changing its value, the y-intercept = 0.

Place the first point at (0,{n}) (The x-value of the y-intercept is always zero.)

2. Use the slope to find a second point.

The slope is {signm}$\frac{{DmNum}}{{DmDen}}$.

First, Start at the y-intercept. Go {mNum} units on the y axis.

{mFB}

Next, go {mDen} on the x-axis. Put your second point at ({mDen},{mNumPb})

]]> L84 - Graph Equation -b = mx - y Graph the equation {=-1*n} = {m}x - y
using the slope and y-intercept. {#A}]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. n={-2,-1,3}; m={-3:0,1:4}; bn={1:99999}; xVals=shuffle([-5,-4,-3,-2,-1,0,1,2,3,4,5]); 0,join("","Go down ",abs(m)," because the slope is negative"),join("","Go up ",abs(m)," because the slope is positive")); xVal=[xVals[0],xVals[1],xVals[2],xVals[3]]; xVal=sort(xVal); x1=xVal[0]; y1=m*x1+n; p1=join("",m,"(",x1,")",pick(n<0,join(""," + ",n),join("",n))); p1S1=join("",m*x1,pick(n<0,join(""," + ",n),join("",n))); p1S1FB=join("","Multiply ",m," and ",x1); p1S2=join("",m*x1+n); p1S2FB=join("",p1S1," = ",p1S2); x2=xVal[1]; y2=m*x2+n; p2=join("",m,"(",x2,")",pick(n<0,join(""," + ",n),join("",n))); p2S1=join("",m*x2,pick(n<0,join(""," + ",n),join("",n))); p2S1FB=join("","Multiply ",m," and ",x2); p2S2=join("",m*x2+n); p2S2FB=join("",p2S1," = ",p2S2); x3=xVal[2]; y3=m*x3+n; p3=join("",m,"(",x3,")",pick(n<0,join(""," + ",n),join("",n))); p3S1=join("",m*x3,pick(n<0,join(""," + ",n),join("",n))); p3S1FB=join("","Multiply ",m," and ",x3); p3S2=join("",m*x3+n); p3S2FB=join("",p3S1," = ",p3S2); x4=xVal[3]; y4=m*x4+n; p4=join("",m,"(",x4,")",pick(n<0,join(""," + ",n),join("",n))); p4S1=join("",m*x4,pick(n<0,join(""," + ",n),join("",n))); p4S1FB=join("","Multiply ",m," and ",x4); p4S2=join("",m*x4+n); p4S2FB=join("",p4S1," = ",p4S2);]]> none 0 #A 1 0 4 [0,n,1,m+n] ((_1==n+m*_0)*.5) + ((_3==n+m*_2)*.5) 1 1

]]>

{=-1*n} = {m}x - y

Given

+y +y

Add y to both sides

{=-1*n} +y = {m}x

{n} {n}

Move {=-1*n} to the right side

y = {m}x + {n}

The equation is now in slope-intercept form.

A line can be graphed from two points.

1. Locate the y-intercept. This is the first point.

2. Use the slope to find a second point.

The first point is the y-intercept.

Place the first point at (0,{n}) (The x-value of the y-intercept is always zero.)

The second point is calculated using the slope.

The slope is {m}. Write the slope as a fraction by writing {m} over 1.

slope = $\frac{Δy}{Δx}$ = $\frac{{m}}{1}$

First, Start at the y-intercept. Go {m} units on the y axis.

{mFB}

Next, go 1 unit on the x-axis. Put your second point at (1,{=m+n})

]]> L84 - Graph Equation 0= mx- y (fractional slope) (y-int of 0)

Graph the linear equation {signm}$\frac{{DmNum}}{{DmDen}}$x - y =0 using the slope and y-intercept.

{#A}]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. mA={[1,2],[1,3],[2,3],[1,4],[2,4],[3,4],[1,5],[2,5],[3,5],[1,6],[2,6],[3,6],[4,6],[5,6],[1,7],[2,7],[3,7],[4,7],[5,7],[6,7],[1,8],[2,8],[3,8],[4,8],[5,8],[6,8],[7,8],[1,10],[2,10],[3,10],[4,10],[5,10],[6,10],[7,10],[8,10],[9,10],[2,1],[3,1],[3,2],[4,1],[4,2],[4,3],[5,1],[5,2],[5,3],[6,1],[6,2],[6,3],[6,4]}; b={-7:-1,1:7}; bn={1:99999}; signM={-1,1}; 0,join("","Go down ",abs(mNum)," because the slope is negative"),join("","Go up ",abs(mNum)," because the slope is positive")); signb=pick(b>=0,"-","+"); disb=abs(b); signm=pick(signM>0,"-",""); DmNum=abs(mNum); DmDen=abs(mDen); mNumPb=mNum+b;]]> none 0 #A 1 0 4 [0,b,mDen,mNum+b] ((_1==b+m*_0)*.5) + ((_3==b+m*_2)*.5) 1 1

]]> {signm}$\frac{{DmNum}}{{DmDen}}$x - y =0 Given + y + y Add y to both sides {signm}$\frac{{DmNum}}{{DmDen}}$x = y the equation is in slope-intercept form A line can be graphed from two points.

1. Locate the y-intercept. This is the first point.

Since 0 can be added to the equation without changing its value, the y-intercept = 0.

Place the first point at (0,{n}) (The x-value of the y-intercept is always zero.)

2. Use the slope to find a second point.

The slope is {signm}$\frac{{DmNum}}{{DmDen}}$.

First, Start at the y-intercept. Go {mNum} units on the y axis.

{mFB}

Next, go {mDen} on the x-axis. Put your second point at ({mDen},{mNumPb})

]]> L84 - Graph Equation y-b=mx (fractional slope)

Graph the linear equation y {signDisb} {disb}={signm}$\frac{{DmNum}}{{DmDen}}$x using the slope and y-intercept.

{#A}]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. mA={[1,2],[1,3],[2,3],[1,4],[2,4],[3,4],[1,5],[2,5],[3,5],[1,6],[2,6],[3,6],[4,6],[5,6],[1,7],[2,7],[3,7],[4,7],[5,7],[6,7],[1,8],[2,8],[3,8],[4,8],[5,8],[6,8],[7,8],[1,10],[2,10],[3,10],[4,10],[5,10],[6,10],[7,10],[8,10],[9,10],[2,1],[3,1],[3,2],[4,1],[4,2],[4,3],[5,1],[5,2],[5,3],[6,1],[6,2],[6,3],[6,4]}; b={-7:-1,1:7}; bn={1:99999}; signM={-1,1}; 0,join("","Go down ",abs(mNum)," because the slope is negative"),join("","Go up ",abs(mNum)," because the slope is positive")); signb=pick(b>0,"-","+"); signDisb=pick(b>0,"+","-"); disb=abs(b); signm=pick(signM>0,"-",""); DmNum=abs(mNum); DmDen=abs(mDen); mNumPb=mNum+b;]]> none 0 #A 1 0 4 [0,b,mDen,mNum+b] ((_1==b+m*_0)*.5) + ((_3==b+m*_2)*.5) 1 1

]]> y {signDisb} {disb}={signm}$\frac{{DmNum}}{{DmDen}}$x Given {signb} {disb} {signb} {disb} y ={signm}$\frac{{DmNum}}{{DmDen}}$x {signb} {disb} Slope - Intercept Form A line can be graphed from two points.

1. Locate the y-intercept. This is the first point.

Place the first point at (0,{n}) (The x-value of the y-intercept is always zero.)

2. Use the slope to find a second point.

The slope is {signm}$\frac{{DmNum}}{{DmDen}}$.

First, Start at the y-intercept. Go {mNum} units on the y axis.

{mFB}

Next, go {mDen} on the x-axis. Put your second point at ({mDen},{mNumPb})

]]> L84 - Graph Equation y=mx+b (y-int of 0) Graph the equation $\frac{y}{{m}}$ = x
using the slope and y-intercept. {#A}]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. n={-2,-1,3}; m={-3:0,1:4}; bn={1:99999}; xVals=shuffle([-5,-4,-3,-2,-1,0,1,2,3,4,5]); 0,join("","Go down ",abs(m)," because the slope is negative"),join("","Go up ",abs(m)," because the slope is positive"));]]> none 0 #A 1 0 4 [0,n,1,m+n] ((_1==n+m*_0)*.5) + ((_3==n+m*_2)*.5) 1 1

]]> $\frac{y}{{m}}$ = x Given

{m}($\frac{y}{{m}}$) =({m}) x

Multiply both sides by {m} y = {m}x The Equation is in slope-intercept form.

A line can be graphed from two points.

1. Locate the y-intercept. This is the first point.

2. Use the slope to find a second point.

The first point is the y-intercept.

Place the first point at (0,{n}) (The x-value of the y-intercept is always zero.)

The second point is calculated using the slope.

The slope is {m}. Write the slope as a fraction by writing {m} over 1.

slope = $\frac{Δy}{Δx}$ = $\frac{{m}}{1}$

First, Start at the y-intercept. Go {m} units on the y axis.

{mFB}

Next, go 1 unit on the x-axis. Put your second point at (1,{=m+n})

]]> L84- line-yInt-Slope-Equation Give the y-intercept, slope and equation of the line. y {signOb} {disb} = $\frac{{mNum}}{{mDen}}$x]]> var board = JXG.JSXGraph.initBoard(BOARDID,{ axis:true,grid:true, boundingbox: [-11,11,11,-11], showCopyright: false, showNavigation: false }); var graph = board.create('functiongraph', [function(x){ return {m}*x+{b};}, -10,10],{firstArrow:true,lastArrow:true,strokeColor:'green'}); var yInt=board.create('point',[0,{b}],{size:3,fillOpacity:0,strokeColor:'orange',name:''}); var ansY=board.create('line',[[0,{b}],[0,{b}+{mNum}]],{strokeColor:'red',straightFirst:false,straightLast:false,firstArrow:false,lastArrow:{type:2,size:4}}); var ansX=board.create('line',[[0,{b}+{mNum}],[{mDen},{b}+{mNum}]],{strokeColor:'blue',straightFirst:false,straightLast:false,firstArrow:false,lastArrow:{type:2,size:4}}); ]]> 3.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. mA={[1,2],[1,3],[2,3],[1,4],[2,4],[3,4],[1,5],[2,5],[3,5],[1,6],[2,6],[3,6],[4,6],[5,6],[1,7],[2,7],[3,7],[4,7],[5,7],[6,7],[1,8],[2,8],[3,8],[4,8],[5,8],[6,8],[7,8],[1,10],[2,10],[3,10],[4,10],[5,10],[6,10],[7,10],[8,10],[9,10],[2,1],[3,1],[3,2],[4,1],[4,2],[4,3],[5,1],[5,2],[5,3],[6,1],[6,2],[6,3],[6,4]}; b={-7:7}; n={-2,3}; bn={1:99999}; direction={0,1}; 0,"-","+"); signOb=pick(b>0,"+","-"); disb=abs(b); chSign=["positive","negative"]; chDir=["up","down"]; ansB=pick(b>0,1,0);]]> none 0 1 0 3 [b,0,b] _err == 0 1 1 The order pair of the y-intercept is ({_1},{_2})
]]> Write the equation in slope-intercept form.

y {signOb} {disb} = $\frac{{mNum}}{{mDen}}$x		Given
{signb} {disb} {signb} {disb}		Move {disb} to the right side
y= $\frac{{mNum}}{{mDen}}$x {signb} {disb}		The equation is in Slope-Intercept form

The y-intercept is {b}.
The ordered pair of the y-intercept is (0,{b}).

]]> 1 1 0 2 [mNum,mDen] _err == 0 1 1 The slope is {_0} {_1} ]]> The slope is $\frac{{mNum}}{{mDen}}$.

The change in y is {mNum}.	Slope =	{mNum}
The change in x is {mDen}.	Slope =	{mDen}

]]> 2 1 0 4 [mNum,mDen,ansB,ansB] _err == 0 1 1 The change in y is {_0}.

The change in x is {_1}

The slope is {_2:chSign:MCE}, therefore go {_3:chDir:MCE} in the y-direction.

]]>

The change in y is {mNum}.

The change in x is {mDen}.

The slope is {=chSign[ansB]}, therefore go {=chDir[ansB]} in the y-direction.

]]> L84-Name slope mDeny=mNumx + b(mDen) Give the slope of the linear equation. {mDen}y={mNum}x + {=mDen*b}

]]> {mDen}y={mNum}x + {=mDen*b} Given $\frac{{mDen}y}{{mDen}}$=$\frac{{mNum}x}{{mDen}}$ + $\frac{{=mDen*b}}{{mDen}}$ Divide each term by {mDen} y=$\frac{{mNum}}{{mDen}}$x + {b}

y=$\frac{{mNum}}{{mDen}}$x + {b}

The slope is $\frac{{mNum}}{{mDen}}$.

The change in y is {mNum}.	Slope =	{mNum}
The change in x is {mDen}.	Slope =	{mDen}

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. mA={[1,2],[1,3],[2,3],[1,4],[2,4],[3,4],[1,5],[2,5],[3,5],[1,6],[2,6],[3,6],[4,6],[5,6],[1,7],[2,7],[3,7],[4,7],[5,7],[6,7],[1,8],[2,8],[3,8],[4,8],[5,8],[6,8],[7,8],[1,10],[2,10],[3,10],[4,10],[5,10],[6,10],[7,10],[8,10],[9,10],[2,1],[3,1],[3,2],[4,1],[4,2],[4,3],[5,1],[5,2],[5,3],[6,1],[6,2],[6,3],[6,4]}; b={-7:7}; bn={1:99999}; slope={-1,1}; 0,"less than zero, it is negative","greater than zero, it is positive"); m=mA[0]/mA[1]; MB=join("","MyBoxH1",bn); mNum=mA[0]; mDen=mA[1]; GCF=gcd(mNum,mDen); mNum=-1*mNum/GCF; mDen=mDen/GCF; m=mNum/mDen;]]> none 0 1 0 2 [mNum,mDen] _err == 0 1 1 The slope is {_0}{_1}]]> L84-Name y-Intercept y-mx = b Give the ordered pair of the y-intercept of the linear equation
y- $\frac{{mNum}}{{mDen}}$x = {signB} {absB}

]]> The y-intercept is where the equation crosses the y-axis.
y={m}x {signB} {absB}
The y-intercept is at (0,{b}).

]]> Divide both sides of the equation by {mDen} to write the equation in slope-intercept form.

y=$\frac{{mNum}}{{mDen}}$x

The y-intercept is where the equation crosses the y-axis.
y=$\frac{{mNum}}{{mDen}}$x {signB} {absB}
The identity property of addition is zero. adding zero does not change the sum.
The y-intercept is at (0,{b}).

]]> {mDen}y={mNum}x + {=mDen*b} Given $\frac{{mDen}y}{{mDen}}$=$\frac{{mNum}x}{{mDen}}$ + $\frac{{=mDen*b}}{{mDen}}$ Divide each term by {mDen} y=$\frac{{mNum}}{{mDen}}$x + {b}

y=$\frac{{mNum}}{{mDen}}$x + {b}

The slope is $\frac{{mNum}}{{mDen}}$.

The change in y is {mNum}.	Slope =	{mNum}
The change in x is {mDen}.	Slope =	{mDen}

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. mA={[1,2],[1,3],[2,3],[1,4],[2,4],[3,4],[1,5],[2,5],[3,5],[1,6],[2,6],[3,6],[4,6],[5,6],[1,7],[2,7],[3,7],[4,7],[5,7],[6,7],[1,8],[2,8],[3,8],[4,8],[5,8],[6,8],[7,8],[1,10],[2,10],[3,10],[4,10],[5,10],[6,10],[7,10],[8,10],[9,10],[2,1],[3,1],[3,2],[4,1],[4,2],[4,3],[5,1],[5,2],[5,3],[6,1],[6,2],[6,3],[6,4]}; b={-7:7}; bn={1:99999}; slope={-1,1}; 0,"less than zero, it is negative","greater than zero, it is positive"); m=mA[0]/mA[1]; MB=join("","MyBoxH1",bn); mNum=mA[0]; mDen=mA[1]; GCF=gcd(mNum,mDen); mNum=-1*mNum/GCF; mDen=mDen/GCF; m=mNum/mDen;]]> none 0 1 0 2 [mNum,mDen] _err == 0 1 1 The slope is {_0}{_1}]]> $course$/top/Default for MSII/Test #12/L87- dividing Monomials L87-Divide Monomials coef 1(fraction) Simplify: {var1}^{exp1}{var1}^{exp2} ]]> Expand, then multiply.

{num1}{var1}^{exp1}

{num2}{var1}^{exp2}

Given

{num1}{factor1}

{num2}{factor2}

Write the expression as a product of factors

{ansNum}{factorNum}

{factorDen}

Divide the coefficients: {num1}÷{num2}
Cancel each factor that is in the numerator and denominator.

{ansNum}

{var1}^{=abs(ans)}

Write the coefficient.
The base {var1} is multiplied {=abs(exp12)} times

The bases are equal, subtract the exponents

{num1}{var1}^{exp1}

{num2}{var1}^{exp2}

Given

({num1}÷{num2}){var1}^{{exp1}-{exp2}}

Subtract the Exponents
Divide the Coefficients

{ansNum}{var1}^{exp12}

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. smaller),factorNum,join("",factorNum,"•",var1)); factorDen=pick((i<=exp2)&&(i>smaller),factorDen,join("",factorDen,"•",var1)); factor1=pick(i==smaller,factor1,join("","~~",factor1,"~~")); factor2=pick(i==smaller,factor2,join("","~~",factor2,"~~")); } factorDen=join("","1",factorDen); baseLoc=pick(exp1>exp2,pick(exp1==exp2,"in the denominator, therefore it is negative.","The exponent is zero"),"in the numerator, therefore it is positive."); num1T2=num1*num2; a={-100:100}; b={-100:100}; c={-100:100}; d={-100:100}; e={-100:100}; f={-100:100}; g={-100:100}; h={-100:100}; k={-100:100}; m={-100:100}; n={-100:100}; p={-100:100}; r={-100:100}; s={-100:100}; t={-100:100}; v={-100:100}; w={-100:100}; x={-100:100}; y={-100:100}; z={-100:100};]]> abc 0 1 0 1 abs(ans) _err == 0 1 1 {_0}
]]> L87-Divide NEG Number Monomials Simplify: {num1}{var1}^{exp1}{num2}{var1}^{exp2} ]]> Expand, then multiply.

{num1}{var1}^{exp1}

{num2}{var1}^{exp2}

Given

{num1}{factor1}

{num2}{factor2}

Write the expression as a product of factors

{ansNum}{factorNum}

{factorDen}

Divide the coefficients: {num1}÷{num2}
Cancel each factor that is in the numerator and denominator.

{ansNum}{var1}^{exp12}

Write the coefficient.
The base {var1} is multiplied {=abs(exp12)} times {baseLoc}

The bases are equal, subtract the exponents

{num1}{var1}^{exp1}

{num2}{var1}^{exp2}

Given

({num1}÷{num2}){var1}^{{exp1}-{exp2}}

Subtract the Exponents
Divide the Coefficients

{ansNum}{var1}^{exp12}

]]> L87-Divide NEG Number Monomials (fraction) Simplify: {num1}{var1}^{exp1}{num2}{var1}^{exp2} ]]> Expand, then multiply.

{num1}{var1}^{exp1}

{num2}{var1}^{exp2}

Given

{num1}{factor1}

{num2}{factor2}

Write the expression as a product of factors

{ansNum}{factorNum}

{factorDen}

Divide the coefficients: {num1}÷{num2}
Cancel each factor that is in the numerator and denominator.

{ansNum}

{var1}^{=abs(ans)}

Write the coefficient.
The base {var1} is multiplied {=abs(exp12)} times

The bases are equal, subtract the exponents

{num1}{var1}^{exp1}

{num2}{var1}^{exp2}

Given

({num1}÷{num2}){var1}^{{exp1}-{exp2}}

Subtract the Exponents
Divide the Coefficients

{ansNum}{var1}^{exp12}

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. smaller),factorNum,join("",factorNum,"•",var1)); factorDen=pick((i<=exp2)&&(i>smaller),factorDen,join("",factorDen,"•",var1)); factor1=pick(i==smaller,factor1,join("","~~",factor1,"~~")); factor2=pick(i==smaller,factor2,join("","~~",factor2,"~~")); } factorDen=join("","1",factorDen); baseLoc=pick(exp1>exp2,pick(exp1==exp2,"in the denominator, therefore it is negative.","The exponent is zero"),"in the numerator, therefore it is positive."); num1T2=num1*num2; a={-100:100}; b={-100:100}; c={-100:100}; d={-100:100}; e={-100:100}; f={-100:100}; g={-100:100}; h={-100:100}; k={-100:100}; m={-100:100}; n={-100:100}; p={-100:100}; r={-100:100}; s={-100:100}; t={-100:100}; v={-100:100}; w={-100:100}; x={-100:100}; y={-100:100}; z={-100:100};]]> abc 0 1 0 2 [ansNum,abs(ans)] _err == 0 1 1 {_0} {var1}^{_1} ]]> L87-Divide positive exponent Number Monomials Simplify: {num1}{var1}^{exp1}{num2}{var1}^{exp2} ]]> Expand, then multiply.

{num1}{var1}^{exp1}

{num2}{var1}^{exp2}

Given

{num1}{factor1}

{num2}{factor2}

Write the expression as a product of factors

{ansNum}{factorNum}

{factorDen}

Divide the coefficients: {num1}÷{num2}
Cancel each factor that is in the numerator and denominator.

{ansNum}{var1}^{exp12}

Write the coefficient.
The base {var1} is multiplied {=abs(exp12)} times {baseLoc}

The bases are equal, subtract the exponents

{num1}{var1}^{exp1}

{num2}{var1}^{exp2}

Given

({num1}÷{num2}){var1}^{{exp1}-{exp2}}

Subtract the Exponents
Divide the Coefficients

{ansNum}{var1}^{exp12}

]]> TL80-Divide NEG Number Monomials Simplify: {num1}{var1}^{exp1}{num2}{var1}^{exp2} ]]> Expand, then multiply.

{num1}{var1}^{exp1}

{num2}{var1}^{exp2}

Given

{num1}{factor1}

{num2}{factor2}

Write the expression as a product of factors

{ansNum}{factorNum}

{factorDen}

Divide the coefficients: {num1}÷{num2}
Cancel each factor that is in the numerator and denominator.

{ansNum}{var1}^{exp12}

Write the coefficient.
The base {var1} is multiplied {=abs(exp12)} times {baseLoc}

The bases are equal, subtract the exponents

{num1}{var1}^{exp1}

{num2}{var1}^{exp2}

Given

({num1}÷{num2}){var1}^{{exp1}-{exp2}}

Subtract the Exponents
Divide the Coefficients

{ansNum}{var1}^{exp12}

]]> TL80-Divide NEG Number Monomials (fraction) Simplify: {num1}{var1}^{exp1}{num2}{var1}^{exp2} ]]> Expand, then multiply.

{num1}{var1}^{exp1}

{num2}{var1}^{exp2}

Given

{num1}{factor1}

{num2}{factor2}

Write the expression as a product of factors

{ansNum}{factorNum}

{factorDen}

Divide the coefficients: {num1}÷{num2}
Cancel each factor that is in the numerator and denominator.

{ansNum}

{var1}^{=abs(ans)}

Write the coefficient.
The base {var1} is multiplied {=abs(exp12)} times

The bases are equal, subtract the exponents

{num1}{var1}^{exp1}

{num2}{var1}^{exp2}

Given

({num1}÷{num2}){var1}^{{exp1}-{exp2}}

Subtract the Exponents
Divide the Coefficients

{ansNum}{var1}^{exp12}

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. smaller),factorNum,join("",factorNum,"•",var1)); factorDen=pick((i<=exp2)&&(i>smaller),factorDen,join("",factorDen,"•",var1)); factor1=pick(i==smaller,factor1,join("","~~",factor1,"~~")); factor2=pick(i==smaller,factor2,join("","~~",factor2,"~~")); } factorDen=join("","1",factorDen); baseLoc=pick(exp1>exp2,pick(exp1==exp2,"in the denominator, therefore it is negative.","The exponent is zero"),"in the numerator, therefore it is positive."); num1T2=num1*num2; a={-100:100}; b={-100:100}; c={-100:100}; d={-100:100}; e={-100:100}; f={-100:100}; g={-100:100}; h={-100:100}; k={-100:100}; m={-100:100}; n={-100:100}; p={-100:100}; r={-100:100}; s={-100:100}; t={-100:100}; v={-100:100}; w={-100:100}; x={-100:100}; y={-100:100}; z={-100:100};]]> abc 0 1 0 2 [ansNum,abs(ans)] _err == 0 1 1 {_0} {var1}^{_1} ]]> $course$/top/Default for MSII/Test #12/L86- Dilations L64- Parallelogram- dilation-Id Shape Plot the dilation of the quadrilateral with a ({Xt},{Yt}) scale factor.

]]> 2.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. sideStart={[5, 3, 1, 1],[4, 5, 1, 1],[4, 5, 2, 1],[3, 5, 1, 1],[3, 5, 2, 1],[3, 5, 3, 1],[2, 5, 1, 1],[2, 5, 2, 1],[2, 5, 3, 1],[2, 5, 4, 1],[1, 5, 1, 1],[1, 5, 2, 1],[1, 5, 3, 1],[1, 5, 4, 1],[1, 5, 5, 1],[5, 4, 1, 1],[5, 2, 1, 1],[5, 2, 1, 2],[5, 3, 1, 2],[5, 3, 1, 3],[3, 4, 1, 1],[3, 4, 2, 1],[3, 4, 3, 1],[3, 4, 1, 2],[3, 4, 2, 2],[3, 4, 3, 2],[3, 4, 1, 2],[3, 4, 2, 2],[3, 4, 3, 2],[2, 4, 1, 1],[2, 4, 2, 1],[2, 4, 3, 1],[2, 4, 4, 1],[2, 4, 1, 2],[2, 4, 2, 2],[2, 4, 3, 2],[2, 4, 4, 2],[2, 3, 1, 3],[2, 3, 2, 3],[2, 3, 3, 3],[2, 3, 4, 3],[1, 2, 1, 4],[1, 2, 2, 4],[3,2, 3, 4],[1, 2, 4, 4],[1, 4, 1, 1],[1, 4, 2, 1],[1, 4, 3, 1],[1, 4, 4, 1],[1, 4, 5, 1],[1, 4, 1, 2],[1, 4, 2, 2],[1, 4, 3, 2],[1, 4, 4, 2],[1, 4, 5, 2],[1, 4, 1, 3],[1, 4, 2, 3],[1, 4, 3, 3],[1, 4, 4, 2],[1, 4, 5, 1],[1, 4, 1, 2],[1, 4, 2, 2],[1, 4, 3, 2],[1, 4, 4, 2],[1, 4, 5, 1],[1, 4, 1, 1],[1, 4, 2, 1],[1, 4, 3, 2],[1, 4, 4, 2],[1, 4, 5, 2],[5, 3, 1, 1],[4, 3, 1, 1],[4, 3, 2, 1],[4, 3, 1, 2],[4, 3, 2, 2],[2, 3, 1, 1],[2, 3, 2, 1],[2, 3, 3, 1],[2, 3, 4, 1],[2, 3, 1, 2],[2, 3, 2, 2],[2, 3, 3, 2],[2, 3, 4, 2],[2, 3, 1, 3],[2, 3, 2, 3],[2, 3, 3, 3],[2, 3, 4, 3],[2, 3, 1, 4],[2, 3, 2, 4],[2, 3, 3, 4],[2, 3, 4, 1],[1, 3, 1, 1],[1, 3, 2, 1],[1, 3, 3, 1],[1, 3, 4, 1],[1, 3, 5, 1],[1, 3, 1, 2],[1, 3, 2, 2],[1, 3, 3, 2],[1, 3, 4, 2],[1, 3, 5, 2],[1, 3, 1, 3],[1, 3, 2, 3],[1, 3, 3, 3],[1, 3, 4, 3],[1, 3, 5, 3],[1, 3, 1, 1],[1, 3, 2, 3],[1, 3, 3, 4],[1, 3, 4, 2],[1, 3, 5, 1],[1, 3, 1, 3],[1, 3, 2, 2],[2, 1, 3, 5],[1, 3, 4, 2],[1, 3, 5, 1]}; #0= x-axis and 1=y-axis axisRand={0,1}; randShape=shuffle([0,1,2,3,4,5]); bn={1:99999}; randMove=shuffle([-1,1]); Xt={2,3}; Yt={2,3}; none 0 1 0 8 [Xa,Ya,Xb,Yb,Xc,Yc,Xd,Yd] crita+critb+critc+critd 1 1

]]>

To graph the dilation of the quadrilateral ({Xt},{Yt}).

point A is at ({Xa1},{Ya1}) therefore the dilation is at ({Xa},{Ya}).

point B is at ({Xb1},{Yb1}) therefore the dilation is at ({Xb},{Yb}).

point C is at ({Xc1},{Yc1}) therefore the dilation is at ({Xc},{Yc}).

point D is at ({Xd1},{Yd1}) therefore the dilation is at ({Xd},{Yd}).

]]> 1 1 0 1 ans randShape[_0] == correct 1 1 Quadrilateral ABCD is best defined as a {_0:choices:MCE}
Give the best, most specific description.

]]> Quadrilateral ABCD is best defined as a {=shape[correct]}

]]> L64- Parallelogram- dilation-Id Shape Plot the dilation of the quadrilateral ({Xt},{Yt}).

]]>

To graph the dilation of the quadrilateral ({Xt},{Yt}).

point A is at ({Xa1},{Ya1}) therefore the dilation is at ({Xa},{Ya}).

point B is at ({Xb1},{Yb1}) therefore the dilation is at ({Xb},{Yb}).

point C is at ({Xc1},{Yc1}) therefore the dilation is at ({Xc},{Yc}).

point D is at ({Xd1},{Yd1}) therefore the dilation is at ({Xd},{Yd}).

]]> 1 1 0 1 ans randShape[_0] == correct 1 1 Quadrilateral ABCD is best defined as a {_0:choices:MCE}
Give the best, most specific description.

]]> Quadrilateral ABCD is best defined as a {=shape[correct]}

]]> L64- Quadrilateral- dilation-Id Shape Plot the dilation of the quadrilateral with a ({Xt},{Yt}) scale factor.

]]> 2.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. sideStart={[5, 3, 1, 1],[4, 5, 1, 1],[4, 5, 2, 1],[3, 5, 1, 1],[3, 5, 2, 1],[3, 5, 3, 1],[2, 5, 1, 1],[2, 5, 2, 1],[2, 5, 3, 1],[2, 5, 4, 1],[1, 5, 1, 1],[1, 5, 2, 1],[1, 5, 3, 1],[1, 5, 4, 1],[1, 5, 5, 1],[5, 4, 1, 1],[5, 2, 1, 1],[5, 2, 1, 2],[5, 3, 1, 2],[5, 3, 1, 3],[3, 4, 1, 1],[3, 4, 2, 1],[3, 4, 3, 1],[3, 4, 1, 2],[3, 4, 2, 2],[3, 4, 3, 2],[3, 4, 1, 2],[3, 4, 2, 2],[3, 4, 3, 2],[2, 4, 1, 1],[2, 4, 2, 1],[2, 4, 3, 1],[2, 4, 4, 1],[2, 4, 1, 2],[2, 4, 2, 2],[2, 4, 3, 2],[2, 4, 4, 2],[2, 3, 1, 3],[2, 3, 2, 3],[2, 3, 3, 3],[2, 3, 4, 3],[1, 2, 1, 4],[1, 2, 2, 4],[3,2, 3, 4],[1, 2, 4, 4],[1, 4, 1, 1],[1, 4, 2, 1],[1, 4, 3, 1],[1, 4, 4, 1],[1, 4, 5, 1],[1, 4, 1, 2],[1, 4, 2, 2],[1, 4, 3, 2],[1, 4, 4, 2],[1, 4, 5, 2],[1, 4, 1, 3],[1, 4, 2, 3],[1, 4, 3, 3],[1, 4, 4, 2],[1, 4, 5, 1],[1, 4, 1, 2],[1, 4, 2, 2],[1, 4, 3, 2],[1, 4, 4, 2],[1, 4, 5, 1],[1, 4, 1, 1],[1, 4, 2, 1],[1, 4, 3, 2],[1, 4, 4, 2],[1, 4, 5, 2],[5, 3, 1, 1],[4, 3, 1, 1],[4, 3, 2, 1],[4, 3, 1, 2],[4, 3, 2, 2],[2, 3, 1, 1],[2, 3, 2, 1],[2, 3, 3, 1],[2, 3, 4, 1],[2, 3, 1, 2],[2, 3, 2, 2],[2, 3, 3, 2],[2, 3, 4, 2],[2, 3, 1, 3],[2, 3, 2, 3],[2, 3, 3, 3],[2, 3, 4, 3],[2, 3, 1, 4],[2, 3, 2, 4],[2, 3, 3, 4],[2, 3, 4, 1],[1, 3, 1, 1],[1, 3, 2, 1],[1, 3, 3, 1],[1, 3, 4, 1],[1, 3, 5, 1],[1, 3, 1, 2],[1, 3, 2, 2],[1, 3, 3, 2],[1, 3, 4, 2],[1, 3, 5, 2],[1, 3, 1, 3],[1, 3, 2, 3],[1, 3, 3, 3],[1, 3, 4, 3],[1, 3, 5, 3],[1, 3, 1, 1],[1, 3, 2, 3],[1, 3, 3, 4],[1, 3, 4, 2],[1, 3, 5, 1],[1, 3, 1, 3],[1, 3, 2, 2],[2, 1, 3, 5],[1, 3, 4, 2],[1, 3, 5, 1]}; #0= x-axis and 1=y-axis axisRand={0,1}; randShape=shuffle([0,1,2,3,4,5]); bn={1:99999}; randMove=shuffle([-1,1]); Xt={2,3}; Yt={2,3}; offset={1,2,3}; none 0 1 0 8 [Xa,Ya,Xb,Yb,Xc,Yc,Xd,Yd] crita+critb+critc+critd 1 1

]]>

To graph the dilation of the quadrilateral ({Xt},{Yt}).

point A is at ({Xa1},{Ya1}) therefore the dilation is at ({Xa},{Ya}).

point B is at ({Xb1},{Yb1}) therefore the dilation is at ({Xb},{Yb}).

point C is at ({Xc1},{Yc1}) therefore the dilation is at ({Xc},{Yc}).

point D is at ({Xd1},{Yd1}) therefore the dilation is at ({Xd},{Yd}).

]]> 1 1 0 1 ans randShape[_0] == correct 1 1 Quadrilateral ABCD is best defined as a {_0:choices:MCE}
Give the best, most specific description.

]]> Quadrilateral ABCD is best defined as a {=shape[correct]}

]]> L64- Quadrilateral- dilation-Id Shape Plot the dilation of the quadrilateral ({Xt},{Yt}).

]]> 2.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. sideStart={[5, 3, 1, 1],[4, 5, 1, 1],[4, 5, 2, 1],[3, 5, 1, 1],[3, 5, 2, 1],[3, 5, 3, 1],[2, 5, 1, 1],[2, 5, 2, 1],[2, 5, 3, 1],[2, 5, 4, 1],[1, 5, 1, 1],[1, 5, 2, 1],[1, 5, 3, 1],[1, 5, 4, 1],[1, 5, 5, 1],[5, 4, 1, 1],[5, 2, 1, 1],[5, 2, 1, 2],[5, 3, 1, 2],[5, 3, 1, 3],[3, 4, 1, 1],[3, 4, 2, 1],[3, 4, 3, 1],[3, 4, 1, 2],[3, 4, 2, 2],[3, 4, 3, 2],[3, 4, 1, 2],[3, 4, 2, 2],[3, 4, 3, 2],[2, 4, 1, 1],[2, 4, 2, 1],[2, 4, 3, 1],[2, 4, 4, 1],[2, 4, 1, 2],[2, 4, 2, 2],[2, 4, 3, 2],[2, 4, 4, 2],[2, 3, 1, 3],[2, 3, 2, 3],[2, 3, 3, 3],[2, 3, 4, 3],[1, 2, 1, 4],[1, 2, 2, 4],[3,2, 3, 4],[1, 2, 4, 4],[1, 4, 1, 1],[1, 4, 2, 1],[1, 4, 3, 1],[1, 4, 4, 1],[1, 4, 5, 1],[1, 4, 1, 2],[1, 4, 2, 2],[1, 4, 3, 2],[1, 4, 4, 2],[1, 4, 5, 2],[1, 4, 1, 3],[1, 4, 2, 3],[1, 4, 3, 3],[1, 4, 4, 2],[1, 4, 5, 1],[1, 4, 1, 2],[1, 4, 2, 2],[1, 4, 3, 2],[1, 4, 4, 2],[1, 4, 5, 1],[1, 4, 1, 1],[1, 4, 2, 1],[1, 4, 3, 2],[1, 4, 4, 2],[1, 4, 5, 2],[5, 3, 1, 1],[4, 3, 1, 1],[4, 3, 2, 1],[4, 3, 1, 2],[4, 3, 2, 2],[2, 3, 1, 1],[2, 3, 2, 1],[2, 3, 3, 1],[2, 3, 4, 1],[2, 3, 1, 2],[2, 3, 2, 2],[2, 3, 3, 2],[2, 3, 4, 2],[2, 3, 1, 3],[2, 3, 2, 3],[2, 3, 3, 3],[2, 3, 4, 3],[2, 3, 1, 4],[2, 3, 2, 4],[2, 3, 3, 4],[2, 3, 4, 1],[1, 3, 1, 1],[1, 3, 2, 1],[1, 3, 3, 1],[1, 3, 4, 1],[1, 3, 5, 1],[1, 3, 1, 2],[1, 3, 2, 2],[1, 3, 3, 2],[1, 3, 4, 2],[1, 3, 5, 2],[1, 3, 1, 3],[1, 3, 2, 3],[1, 3, 3, 3],[1, 3, 4, 3],[1, 3, 5, 3],[1, 3, 1, 1],[1, 3, 2, 3],[1, 3, 3, 4],[1, 3, 4, 2],[1, 3, 5, 1],[1, 3, 1, 3],[1, 3, 2, 2],[2, 1, 3, 5],[1, 3, 4, 2],[1, 3, 5, 1]}; #0= x-axis and 1=y-axis axisRand={0,1}; randShape=shuffle([0,1,2,3,4,5]); bn={1:99999}; randMove=shuffle([-1,1]); Xt={2,3}; Yt={2,3}; offset={1,2,3}; none 0 1 0 8 [Xa,Ya,Xb,Yb,Xc,Yc,Xd,Yd] crita+critb+critc+critd 1 1

]]>

To graph the dilation of the quadrilateral ({Xt},{Yt}).

point A is at ({Xa1},{Ya1}) therefore the dilation is at ({Xa},{Ya}).

point B is at ({Xb1},{Yb1}) therefore the dilation is at ({Xb},{Yb}).

point C is at ({Xc1},{Yc1}) therefore the dilation is at ({Xc},{Yc}).

point D is at ({Xd1},{Yd1}) therefore the dilation is at ({Xd},{Yd}).

]]> 1 1 0 1 ans randShape[_0] == correct 1 1 Quadrilateral ABCD is best defined as a {_0:choices:MCE}
Give the best, most specific description.

]]> Quadrilateral ABCD is best defined as a {=shape[correct]}

]]> L64- Rectangle- dilation-Id Shape Plot the dilation of the quadrilateral with a ({Xt},{Yt}) scale factor.

]]>

To graph the dilation of the quadrilateral ({Xt},{Yt}).

point A is at ({Xa1},{Ya1}) therefore the dilation is at ({Xa},{Ya}).

point B is at ({Xb1},{Yb1}) therefore the dilation is at ({Xb},{Yb}).

point C is at ({Xc1},{Yc1}) therefore the dilation is at ({Xc},{Yc}).

point D is at ({Xd1},{Yd1}) therefore the dilation is at ({Xd},{Yd}).

]]> 1 1 0 1 ans randShape[_0] == correct 1 1 Quadrilateral ABCD is best defined as a {_0:choices:MCE}
Give the best, most specific description.

]]> Quadrilateral ABCD is best defined as a {=shape[correct]}

]]> L64- Rectangle- dilation-Id Shape Plot the dilation of the quadrilateral ({Xt},{Yt}).

]]>

To graph the dilation of the quadrilateral ({Xt},{Yt}).

point A is at ({Xa1},{Ya1}) therefore the dilation is at ({Xa},{Ya}).

point B is at ({Xb1},{Yb1}) therefore the dilation is at ({Xb},{Yb}).

point C is at ({Xc1},{Yc1}) therefore the dilation is at ({Xc},{Yc}).

point D is at ({Xd1},{Yd1}) therefore the dilation is at ({Xd},{Yd}).

]]> 1 1 0 1 ans randShape[_0] == correct 1 1 Quadrilateral ABCD is best defined as a {_0:choices:MCE}
Give the best, most specific description.

]]> Quadrilateral ABCD is best defined as a {=shape[correct]}

]]> L64- trapezoid- dilation-Id Shape Plot the dilation of the quadrilateral with a ({Xt},{Yt}) scale factor.

]]> 2.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. sideStart={[5, 3, 1, 1],[4, 5, 1, 1],[4, 5, 2, 1],[3, 5, 1, 1],[3, 5, 2, 1],[3, 5, 3, 1],[2, 5, 1, 1],[2, 5, 2, 1],[2, 5, 3, 1],[2, 5, 4, 1],[1, 5, 1, 1],[1, 5, 2, 1],[1, 5, 3, 1],[1, 5, 4, 1],[1, 5, 5, 1],[5, 4, 1, 1],[5, 2, 1, 1],[5, 2, 1, 2],[5, 3, 1, 2],[5, 3, 1, 3],[3, 4, 1, 1],[3, 4, 2, 1],[3, 4, 3, 1],[3, 4, 1, 2],[3, 4, 2, 2],[3, 4, 3, 2],[3, 4, 1, 2],[3, 4, 2, 2],[3, 4, 3, 2],[2, 4, 1, 1],[2, 4, 2, 1],[2, 4, 3, 1],[2, 4, 4, 1],[2, 4, 1, 2],[2, 4, 2, 2],[2, 4, 3, 2],[2, 4, 4, 2],[2, 3, 1, 3],[2, 3, 2, 3],[2, 3, 3, 3],[2, 3, 4, 3],[1, 2, 1, 4],[1, 2, 2, 4],[3,2, 3, 4],[1, 2, 4, 4],[1, 4, 1, 1],[1, 4, 2, 1],[1, 4, 3, 1],[1, 4, 4, 1],[1, 4, 5, 1],[1, 4, 1, 2],[1, 4, 2, 2],[1, 4, 3, 2],[1, 4, 4, 2],[1, 4, 5, 2],[1, 4, 1, 3],[1, 4, 2, 3],[1, 4, 3, 3],[1, 4, 4, 2],[1, 4, 5, 1],[1, 4, 1, 2],[1, 4, 2, 2],[1, 4, 3, 2],[1, 4, 4, 2],[1, 4, 5, 1],[1, 4, 1, 1],[1, 4, 2, 1],[1, 4, 3, 2],[1, 4, 4, 2],[1, 4, 5, 2],[5, 3, 1, 1],[4, 3, 1, 1],[4, 3, 2, 1],[4, 3, 1, 2],[4, 3, 2, 2],[2, 3, 1, 1],[2, 3, 2, 1],[2, 3, 3, 1],[2, 3, 4, 1],[2, 3, 1, 2],[2, 3, 2, 2],[2, 3, 3, 2],[2, 3, 4, 2],[2, 3, 1, 3],[2, 3, 2, 3],[2, 3, 3, 3],[2, 3, 4, 3],[2, 3, 1, 4],[2, 3, 2, 4],[2, 3, 3, 4],[2, 3, 4, 1],[1, 3, 1, 1],[1, 3, 2, 1],[1, 3, 3, 1],[1, 3, 4, 1],[1, 3, 5, 1],[1, 3, 1, 2],[1, 3, 2, 2],[1, 3, 3, 2],[1, 3, 4, 2],[1, 3, 5, 2],[1, 3, 1, 3],[1, 3, 2, 3],[1, 3, 3, 3],[1, 3, 4, 3],[1, 3, 5, 3],[1, 3, 1, 1],[1, 3, 2, 3],[1, 3, 3, 4],[1, 3, 4, 2],[1, 3, 5, 1],[1, 3, 1, 3],[1, 3, 2, 2],[2, 1, 3, 5],[1, 3, 4, 2],[1, 3, 5, 1]}; #0= x-axis and 1=y-axis axisRand={0,1}; randShape=shuffle([0,1,2,3,4,5]); bn={1:99999}; randMove=shuffle([-1,1]); Xt={2,3}; Yt={2,3}; offSet={1,2,3}; none 0 1 0 8 [Xa,Ya,Xb,Yb,Xc,Yc,Xd,Yd] crita+critb+critc+critd 1 1

]]>

To graph the dilation of the quadrilateral ({Xt},{Yt}).

point A is at ({Xa1},{Ya1}) therefore the dilation is at ({Xa},{Ya}).

point B is at ({Xb1},{Yb1}) therefore the dilation is at ({Xb},{Yb}).

point C is at ({Xc1},{Yc1}) therefore the dilation is at ({Xc},{Yc}).

point D is at ({Xd1},{Yd1}) therefore the dilation is at ({Xd},{Yd}).

]]> 1 1 0 1 ans randShape[_0] == correct 1 1 Quadrilateral ABCD is best defined as a {_0:choices:MCE}
Give the best, most specific description.

]]> Quadrilateral ABCD is best defined as a {=shape[correct]}

]]> L64- trapezoid- dilation-Id Shape Plot the dilation of the quadrilateral ({Xt},{Yt}).

]]> 2.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. sideStart={[5, 3, 1, 1],[4, 5, 1, 1],[4, 5, 2, 1],[3, 5, 1, 1],[3, 5, 2, 1],[3, 5, 3, 1],[2, 5, 1, 1],[2, 5, 2, 1],[2, 5, 3, 1],[2, 5, 4, 1],[1, 5, 1, 1],[1, 5, 2, 1],[1, 5, 3, 1],[1, 5, 4, 1],[1, 5, 5, 1],[5, 4, 1, 1],[5, 2, 1, 1],[5, 2, 1, 2],[5, 3, 1, 2],[5, 3, 1, 3],[3, 4, 1, 1],[3, 4, 2, 1],[3, 4, 3, 1],[3, 4, 1, 2],[3, 4, 2, 2],[3, 4, 3, 2],[3, 4, 1, 2],[3, 4, 2, 2],[3, 4, 3, 2],[2, 4, 1, 1],[2, 4, 2, 1],[2, 4, 3, 1],[2, 4, 4, 1],[2, 4, 1, 2],[2, 4, 2, 2],[2, 4, 3, 2],[2, 4, 4, 2],[2, 3, 1, 3],[2, 3, 2, 3],[2, 3, 3, 3],[2, 3, 4, 3],[1, 2, 1, 4],[1, 2, 2, 4],[3,2, 3, 4],[1, 2, 4, 4],[1, 4, 1, 1],[1, 4, 2, 1],[1, 4, 3, 1],[1, 4, 4, 1],[1, 4, 5, 1],[1, 4, 1, 2],[1, 4, 2, 2],[1, 4, 3, 2],[1, 4, 4, 2],[1, 4, 5, 2],[1, 4, 1, 3],[1, 4, 2, 3],[1, 4, 3, 3],[1, 4, 4, 2],[1, 4, 5, 1],[1, 4, 1, 2],[1, 4, 2, 2],[1, 4, 3, 2],[1, 4, 4, 2],[1, 4, 5, 1],[1, 4, 1, 1],[1, 4, 2, 1],[1, 4, 3, 2],[1, 4, 4, 2],[1, 4, 5, 2],[5, 3, 1, 1],[4, 3, 1, 1],[4, 3, 2, 1],[4, 3, 1, 2],[4, 3, 2, 2],[2, 3, 1, 1],[2, 3, 2, 1],[2, 3, 3, 1],[2, 3, 4, 1],[2, 3, 1, 2],[2, 3, 2, 2],[2, 3, 3, 2],[2, 3, 4, 2],[2, 3, 1, 3],[2, 3, 2, 3],[2, 3, 3, 3],[2, 3, 4, 3],[2, 3, 1, 4],[2, 3, 2, 4],[2, 3, 3, 4],[2, 3, 4, 1],[1, 3, 1, 1],[1, 3, 2, 1],[1, 3, 3, 1],[1, 3, 4, 1],[1, 3, 5, 1],[1, 3, 1, 2],[1, 3, 2, 2],[1, 3, 3, 2],[1, 3, 4, 2],[1, 3, 5, 2],[1, 3, 1, 3],[1, 3, 2, 3],[1, 3, 3, 3],[1, 3, 4, 3],[1, 3, 5, 3],[1, 3, 1, 1],[1, 3, 2, 3],[1, 3, 3, 4],[1, 3, 4, 2],[1, 3, 5, 1],[1, 3, 1, 3],[1, 3, 2, 2],[2, 1, 3, 5],[1, 3, 4, 2],[1, 3, 5, 1]}; #0= x-axis and 1=y-axis axisRand={0,1}; randShape=shuffle([0,1,2,3,4,5]); bn={1:99999}; randMove=shuffle([-1,1]); Xt={2,3}; Yt={2,3}; offSet={1,2,3}; none 0 1 0 8 [Xa,Ya,Xb,Yb,Xc,Yc,Xd,Yd] crita+critb+critc+critd 1 1

]]>

To graph the dilation of the quadrilateral ({Xt},{Yt}).

point A is at ({Xa1},{Ya1}) therefore the dilation is at ({Xa},{Ya}).

point B is at ({Xb1},{Yb1}) therefore the dilation is at ({Xb},{Yb}).

point C is at ({Xc1},{Yc1}) therefore the dilation is at ({Xc},{Yc}).

point D is at ({Xd1},{Yd1}) therefore the dilation is at ({Xd},{Yd}).

]]> 1 1 0 1 ans randShape[_0] == correct 1 1 Quadrilateral ABCD is best defined as a {_0:choices:MCE}
Give the best, most specific description.

]]> Quadrilateral ABCD is best defined as a {=shape[correct]}

]]> TL68- Dilation, Translation or Reflection_MC (R) var board=JXG.JSXGraph.initBoard(BOARDID,{ boundingbox:[-12,12,12,0], axis:false, grid:false, showCopyright:false, showNavigation:false, keepaspectratio:true }); var p0=board.create('point',[{Xa},{Ya}],{fixed:true,size:'0',name:'',showInfobox:false}); var p1=board.create('point',[{Xb},{Yb}],{fixed:true,size:'0',name:'',showInfobox:false}); var p2=board.create('point',[{Xc},{Yc}],{fixed:true,size:'0',name:'',showInfobox:false}); var p3=board.create('point',[{Xd},{Yd}],{fixed:true,size:'0',name:'',showInfobox:false}); var poly1=board.create('polygon',[p0,p1,p2,p3],{strokeColor:'{color1}',fillColor:'{color1}',fillOppacity:.25}); var p4=board.create('point',[{Xa1},{Ya1}],{fixed:true,size:'0',name:'',showInfobox:false}); var p5=board.create('point',[{Xb1},{Yb1}],{fixed:true,size:'0',name:'',showInfobox:false}); var p6=board.create('point',[{Xc1},{Yc1}],{fixed:true,size:'0',name:'',showInfobox:false}); var p7=board.create('point',[{Xd1},{Yd1}],{fixed:true,size:'0',name:'',showInfobox:false}); var poly2=board.create('polygon',[p4,p5,p6,p7],{strokeColor:'{color2}',fillColor:'{color2}',fillOppacity:.25}); ]]> The figure is reflected through the line. It is a reflection.

]]> TL86- Dilation-Translation or Reflection_MC (dilation) var board=JXG.JSXGraph.initBoard(BOARDID,{ boundingbox:[0,25,25,0], axis:false, grid:false, showCopyright:false, showNavigation:false, keepaspectratio:true }); var p0=board.create('point',[{Xa},{Ya}],{fixed:true,size:'0',name:'',showInfobox:false}); var p1=board.create('point',[{Xb},{Yb}],{fixed:true,size:'0',name:'',showInfobox:false}); var p2=board.create('point',[{Xc},{Yc}],{fixed:true,size:'0',name:'',showInfobox:false}); var p3=board.create('point',[{Xd},{Yd}],{fixed:true,size:'0',name:'',showInfobox:false}); var poly1=board.create('polygon',[p0,p1,p2,p3],{strokeColor:'{color1}',fillColor:'{color1}',fillOppacity:.25}); var p4=board.create('point',[{Xa1},{Ya1}],{fixed:true,size:'0',name:'',showInfobox:false}); var p5=board.create('point',[{Xb1},{Yb1}],{fixed:true,size:'0',name:'',showInfobox:false}); var p6=board.create('point',[{Xc1},{Yc1}],{fixed:true,size:'0',name:'',showInfobox:false}); var p7=board.create('point',[{Xd1},{Yd1}],{fixed:true,size:'0',name:'',showInfobox:false}); var poly2=board.create('polygon',[p4,p5,p6,p7],{strokeColor:'{color2}',fillColor:'{color2}',fillOppacity:.25}); ]]> The {color1} figure is stretched, or made larger. It is a dilation.

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. 0,join("",abs(Xt)," to the left"),join("",abs(Xt)," to the right")); yMove=pick(Yt>0,join("",abs(Yt)," down"),join("",abs(Yt)," up")); Xa=Xa1*Xt; Ya=Ya1*Yt; Xb=Xb1*Xt; Yb=Yb1*Yt; Xc=Xc1*Xt; Yc=Yc1*Yt; Xd=Xd1*Xt; Yd=Yd1*Yt; MB=join("","MyBoxH1",bn); s=join("","A:(",Xa,",",Ya,"), B:(",Xb,",",Yb,"), C:(",Xc,",",Yc,"), D:(",Xd,",",Yd,")"); shape=["square","rectangle","trapezoid", "quadrilateral", "parallelogram", "rhombus"]; choices=[shape[randShape[0]],shape[randShape[1]],shape[randShape[2]],shape[randShape[3]],shape[randShape[4]],shape[randShape[5]]]; ans=-1; for (i:[0:6]){ ans=(randShape[i]==correct)?i:ans; } xArray=[Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1]; yArray=[Ya,Yb,Yc,Yd,Ya1,Yb1,Yc1,Yd1]; lowX=100; lowY=100; maxX=-1; maxY=-1; for (i:[0:8]){ lowX=(xArray[i]maxX)?i:maxX; maxY=(yArray[i]>maxY)?i:maxY; } maxX=maxX+1; maxY=maxY+1; loxX=lowX-1; lowY=lowY-1; height=((maxY-lowY)*400)/(maxX-lowX); choices=["translation","reflection","dilation"];]]> none 0 1 0 1 2 _err == 0 1 1 What transformation is shown? {_0:choices}

]]> TL86- Dilation-Translation or Reflection_MC (trans) var board=JXG.JSXGraph.initBoard(BOARDID,{ boundingbox:[0,12,12,0], axis:false, grid:false, showCopyright:false, showNavigation:false, keepaspectratio:true }); var p0=board.create('point',[{Xa},{Ya}],{fixed:true,size:'0',name:'',showInfobox:false}); var p1=board.create('point',[{Xb},{Yb}],{fixed:true,size:'0',name:'',showInfobox:false}); var p2=board.create('point',[{Xc},{Yc}],{fixed:true,size:'0',name:'',showInfobox:false}); var p3=board.create('point',[{Xd},{Yd}],{fixed:true,size:'0',name:'',showInfobox:false}); var poly1=board.create('polygon',[p0,p1,p2,p3],{strokeColor:'{color1}',fillColor:'{color1}',fillOppacity:.25}); var p4=board.create('point',[{Xa1},{Ya1}],{fixed:true,size:'0',name:'',showInfobox:false}); var p5=board.create('point',[{Xb1},{Yb1}],{fixed:true,size:'0',name:'',showInfobox:false}); var p6=board.create('point',[{Xc1},{Yc1}],{fixed:true,size:'0',name:'',showInfobox:false}); var p7=board.create('point',[{Xd1},{Yd1}],{fixed:true,size:'0',name:'',showInfobox:false}); var poly2=board.create('polygon',[p4,p5,p6,p7],{strokeColor:'{color2}',fillColor:'{color2}',fillOppacity:.25}); ]]> The {color2} figure is moved to the right, and up. It is a translation.

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. 0,join("",abs(Xt)," to the left"),join("",abs(Xt)," to the right")); yMove=pick(Yt>0,join("",abs(Yt)," down"),join("",abs(Yt)," up")); Xa=Xa1+Xt; Ya=Ya1+Yt; Xb=Xb1+Xt; Yb=Yb1+Yt; Xc=Xc1+Xt; Yc=Yc1+Yt; Xd=Xd1+Xt; Yd=Yd1+Yt; MB=join("","MyBoxH1",bn); s=join("","A:(",Xa,",",Ya,"), B:(",Xb,",",Yb,"), C:(",Xc,",",Yc,"), D:(",Xd,",",Yd,")"); shape=["square","rectangle","trapezoid", "quadrilateral", "parallelogram", "rhombus"]; choices=[shape[randShape[0]],shape[randShape[1]],shape[randShape[2]],shape[randShape[3]],shape[randShape[4]],shape[randShape[5]]]; ans=-1; for (i:[0:6]){ ans=(randShape[i]==correct)?i:ans; } xArray=[Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1]; yArray=[Ya,Yb,Yc,Yd,Ya1,Yb1,Yc1,Yd1]; lowX=100; lowY=100; maxX=-1; maxY=-1; for (i:[0:8]){ lowX=(xArray[i]maxX)?i:maxX; maxY=(yArray[i]>maxY)?i:maxY; } maxX=maxX+1; maxY=maxY+1; loxX=lowX-1; lowY=lowY-1; height=((maxY-lowY)*400)/(maxX-lowX); choices=["translation","reflection","dilation"];]]> none 0 1 0 1 0 _err == 0 1 1 What transformation is shown? {_0:choices}

]]> $course$/top/Default for MSII/Test #12/L88-Problem Solving TL88- Product and Sum of two numbers find two numbers The sum of two numbers equals {sumNum}. The product of the numbers is {prodNum}. What are the two numbers?

]]> The numbers are {number1} and {number2}.

The sum of the numbers: {number1} + {number2} = {sumNum}

The product of the numbers: ({number1})({number2}) = {prodNum}

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. number1={2:20:1}; number2={2:20:1}; sumNum=number1+number2; prodNum=number1*number2; abc 0 1 0 2 [number1,number2] 1 1 The numbers are {_0} and {_1}.

]]> TL88- Fertilizer for Garden {name} has a circular garden with a diameter of {diameter} feet. She is using a new fertilizer. If she uses {teaspoon} teaspoons for every {sqfeet} square feet of garden, how much will {name} need for her entire garden? Round to the nearest tenth.

]]>

The circular garden has a diameter of {diameter} feet.
Calculate the radius.
The Area is A=$\pi$r²
{teaspoon} teaspoons for every {sqfeet} square feet of garden

1. Calculate the radius of the garden
2. Find the Area of the garden
3. Divide by the treatment square feet ({sqfeet} square feet)
4. Multiply by the number of teaspoons to use ({teaspoon} teaspoons)

1. Calculate the radius of the garden
radius = diameter ÷ 2 = {diameter} ÷ 2 = {radius}

2. Calculate the area of the garden
A= $\pi$r²
A = (3.14)({radius})²
A={area} square feet.

3. Divide the area of the garden by the treatment size
Area ÷ treatment size
{area} square feet ÷ {sqfeet} square feet = {numSpoon}

4. Calculate the number of teaspoons needed
{numSpoon} times {teaspoon} teaspoons
({numSpoon})({teaspoon}) = {total} teaspoons

The garden is {area} square feet.
For each {sqfeet} square feet {teaspoon} teaspoons of fertilizer must be added.
It makes sense that {total} teaspoons of fertilizer must be added. ]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. radius=diameter/2; area=3.14*radius*radius; numSpoon=area/sqfeet; total=teaspoon*numSpoon; abc 0 1 0 1 round(total,1) _err == 0 1 1 {name} needs {_0} teaspoons.

]]>

The circular garden has a diameter of {diameter} feet.
Calculate the radius.
The Area is A=$\pi$r²
{teaspoon} teaspoons for every {sqfeet} square feet of garden

1. Calculate the radius of the garden
2. Find the Area of the garden
3. Divide by the treatment square feet ({sqfeet} square feet)
4. Multiply by the number of teaspoons to use ({teaspoon} teaspoons)

The garden is {area} square feet.
For each {sqfeet} square feet {teaspoon} teaspoons of fertilizer must be added.
It makes sense that {total} teaspoons of fertilizer must be added. ]]> 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1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. radius=diameter/2; area=3.14*radius*radius; numSpoon=area/sqfeet; total=teaspoon*numSpoon; abc 0 1 0 1 round(total,1) _err == 0 1 1 {name} needs {_0} teaspoons.

]]> TL88- Ratios and Percents {Num} out of every {Den} {category} in the town are {specific}. Write this ratio as a percent.

]]> There are a few ways to solve this question:

1. Divide, then multiply by 100: ($\frac{{Num}}{{Den}}$)(100) = ({=Num/Den})(100) = {percent}%

2. Write the Ratio as a fraction, then change the denominator to 100: $\frac{{Num}}{{Den}}$ = $\frac{Percent}{100}$

$\frac{{Num}}{{Den}}$ = {percent} %

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. Num=fraction0[0]; Den=fraction0[1]; category=randCN[0]; specific=randCN[1]; percent=Num/Den*100; abc 0 1 0 1 round(percent,2) 1 1 Round to the nearest hundredth.
{_0}%

]]> TL88- Scale Drawings and Models The local museum is making a scale model of {townName} Town. The scale model is 1 inch = {scale} feet. The {name} tower is {tHeight} feet in {townName} Town. What is the height of the tower in the museum's model town?

]]>

Write down the important information:
The scale model is 1 inch = {scale} feet
The {name} tower = {tHeight} feet
What is the height of the model tower?

Make a Proportion to solve for the height. $\frac{model height}{actual height}$
$\frac{1 inch}{{scale} feet}$ = $\frac{Model Height}{{tHeight} feet}$

Cross Multiply (1 inch)({tHeight} feet) = ({scale} feet)(Model Height)
Divide both sides by ({scale} feet)

(1 inch)({tHeight} ~~feet~~ )	=	(~~{scale}~~ ~~feet~~)(Model Height)
{scale} ~~feet~~	=	~~{scale}~~ ~~feet~~

Cancel out "feet" on both sides.

(1 inch)({tHeight})	=	Model Height
{scale}	=

Divide {tHeight} by {scale}
Model Height = {ans} inches

The scale model is 1 inch = {scale} feet
The {name} tower = {tHeight} feet
What is the height of the model tower?
Since $\frac{1 inch}{{scale} feet}$ = $\frac{{ans} inches}{{tHeight} feet}$ is a true statement, the answer is correct.
]]> 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 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. abc 0 1 0 2 [ans,unit] 1 1 Round to the nearest hundredth.
{_0} {_1:units:MCE}

]]> TL88- Tables pushed together for large group A local park has a picnic area with {numTables} square tables that can be pushed together to form one long table for a large group. Each square table can seat {numPeople} people on each side of the table. How many people can be seated at the combined tables?

]]> The illustration on the computer may show rectangular tables, the are actually square. var board = JXG.JSXGraph.initBoard(BOARDID,{ axis:false,grid:false, boundingbox: [-5,6,20,-2], showCopyright: false, showNavigation: false, keepAspectratio:true }); for (let i=0; i<{numTables}; i++) { board.create('polygon', [[ i*{distance},0],[(i+1)*{distance},0],[(i+1)*{distance},2],[(i)*{distance},2]],{vertices: {withLabel: false,size:0},strokeColor:'black'}); } board.create('polygon', [[ 0,0],[({numTables})*{distance},0],[({numTables})*{distance},2],[0,2]],{vertices: {withLabel: false,size:0},strokeColor:'red'}); board.create('text',[0,2.25,"{numTables} tables times {numPeople} per table = {numTop} people."],{anchorX:'left',anchorY:'bottom'}); board.create('text',[0,-.25,"{numTables} tables times {numPeople} per table = {numTop} people."],{anchorX:'left',anchorY:'top'}); board.create('text',[ -.25,1,"{numPeople} on the left."],{anchorX:'right',anchorY:'middle'}); board.create('text',[({numTables})*{distance}+.25,1,"{numPeople} on the right."],{anchorX:'left',anchorY:'middle'});
Add up the number of people that can sit at the long table: {numTop} + {numTop} + {numPeople} + {numPeople} = {total} people
{numTables} tables pushed together can fit {total} people.]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. numTables={8:26:1}; numPeople={2,3,4,5}; total=(2*numTables+2)*numPeople; distance=numTables/16; numTop=numTables*numPeople; numLR=numPeople*2; abc 0 1 0 1 total _err == 0 1 1 The total number of people that can sit at the long table is {_0} people.

]]> TL88- Tables pushed together for large group A local park has a picnic area with {numTables} square tables that can be pushed together to form one long table for a large group. Each square table can seat {numPeople} people. How many people can be seated at the combined tables?

]]> TL88-Brick building {name1} can lay {b1} bricks in one hour. {name2} can lay {b2} bricks in one hour. {name3} can lay {b3} bricks in one hour. About how long will it them to build a structure that uses {numBricks} bricks?

]]>

{name1} can lay {b1} bricks in one hour.
{name2} can lay {b2} bricks in one hour.
{name3} can lay {b3} bricks in one hour.
About how long will it them to build a structure that uses {numBricks} bricks?

In one hour the three can lay {total} bricks
Divide {numBricks} by {total} to determine how many hours it will take to lay all the bricks.

{numBricks} ÷ {total} = {hours} hours
Round the number of hours to the nearest half hour.

Use the answer to determine if it make sense.
Each hour the three can lay {total} bricks.
In {hours} hours they can lay {numBricks} bricks.]]> 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 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. total=b1+b2+b3; numBricks=floor(total*hours); abc 0 1 0 1 hours _err == 0 1 1 Round the answer to the nearest half-hour. (1.5 means one and one-half hours)
It takes about {_0} hours for them to lay {numBricks}

]]> $course$/top/Default for MSII/Test #12/L86- Dilations/L86- Dilation-Reflection-Translation- Multiple Choice TL68- Dilation, Translation or Reflection_MC (R) var board=JXG.JSXGraph.initBoard(BOARDID,{ boundingbox:[-12,12,12,0], axis:false, grid:false, showCopyright:false, showNavigation:false, keepaspectratio:true }); var p0=board.create('point',[{Xa},{Ya}],{fixed:true,size:'0',name:'',showInfobox:false}); var p1=board.create('point',[{Xb},{Yb}],{fixed:true,size:'0',name:'',showInfobox:false}); var p2=board.create('point',[{Xc},{Yc}],{fixed:true,size:'0',name:'',showInfobox:false}); var p3=board.create('point',[{Xd},{Yd}],{fixed:true,size:'0',name:'',showInfobox:false}); var poly1=board.create('polygon',[p0,p1,p2,p3],{strokeColor:'{color1}',fillColor:'{color1}',fillOppacity:.25}); var p4=board.create('point',[{Xa1},{Ya1}],{fixed:true,size:'0',name:'',showInfobox:false}); var p5=board.create('point',[{Xb1},{Yb1}],{fixed:true,size:'0',name:'',showInfobox:false}); var p6=board.create('point',[{Xc1},{Yc1}],{fixed:true,size:'0',name:'',showInfobox:false}); var p7=board.create('point',[{Xd1},{Yd1}],{fixed:true,size:'0',name:'',showInfobox:false}); var poly2=board.create('polygon',[p4,p5,p6,p7],{strokeColor:'{color2}',fillColor:'{color2}',fillOppacity:.25}); ]]> The figure is reflected through the line. It is a reflection.

]]> TL68- Translation or Reflection or dilation_MC (dilation) var board=JXG.JSXGraph.initBoard(BOARDID,{ boundingbox:[0,30,30,0], axis:false, grid:false, showCopyright:false, showNavigation:false, keepaspectratio:true }); var p0=board.create('point',[{Xa},{Ya}],{fixed:true,size:'0',name:'',showInfobox:false}); var p1=board.create('point',[{Xb},{Yb}],{fixed:true,size:'0',name:'',showInfobox:false}); var p2=board.create('point',[{Xc},{Yc}],{fixed:true,size:'0',name:'',showInfobox:false}); var p3=board.create('point',[{Xd},{Yd}],{fixed:true,size:'0',name:'',showInfobox:false}); var poly1=board.create('polygon',[p0,p1,p2,p3],{strokeColor:'{color1}',fillColor:'{color1}',fillOppacity:.25}); var p4=board.create('point',[{Xa1},{Ya1}],{fixed:true,size:'0',name:'',showInfobox:false}); var p5=board.create('point',[{Xb1},{Yb1}],{fixed:true,size:'0',name:'',showInfobox:false}); var p6=board.create('point',[{Xc1},{Yc1}],{fixed:true,size:'0',name:'',showInfobox:false}); var p7=board.create('point',[{Xd1},{Yd1}],{fixed:true,size:'0',name:'',showInfobox:false}); var poly2=board.create('polygon',[p4,p5,p6,p7],{strokeColor:'{color2}',fillColor:'{color2}',fillOppacity:.25}); ]]> The {color2} figure is moved to the right, and up. It is a translation.

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. 0,join("",abs(Xt)," to the left"),join("",abs(Xt)," to the right")); yMove=pick(Yt>0,join("",abs(Yt)," down"),join("",abs(Yt)," up")); Xa=3+Xa1*Xt; Ya=3+Ya1*Yt; Xb=3+Xb1*Xt; Yb=3+Yb1*Yt; Xc=3+Xc1*Xt; Yc=3+Yc1*Yt; Xd=3+Xd1*Xt; Yd=3+Yd1*Yt; MB=join("","MyBoxH1",bn); s=join("","A:(",Xa,",",Ya,"), B:(",Xb,",",Yb,"), C:(",Xc,",",Yc,"), D:(",Xd,",",Yd,")"); shape=["square","rectangle","trapezoid", "quadrilateral", "parallelogram", "rhombus"]; choices=[shape[randShape[0]],shape[randShape[1]],shape[randShape[2]],shape[randShape[3]],shape[randShape[4]],shape[randShape[5]]]; ans=-1; for (i:[0:6]){ ans=(randShape[i]==correct)?i:ans; } xArray=[Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1]; yArray=[Ya,Yb,Yc,Yd,Ya1,Yb1,Yc1,Yd1]; lowX=100; lowY=100; maxX=-1; maxY=-1; for (i:[0:8]){ lowX=(xArray[i]maxX)?i:maxX; maxY=(yArray[i]>maxY)?i:maxY; } maxX=maxX+1; maxY=maxY+1; loxX=lowX-1; lowY=lowY-1; height=((maxY-lowY)*400)/(maxX-lowX); choices=["translation","reflection","dilation"];]]> none 0 1 0 1 2 _err == 0 1 1 What transformation is shown? {_0:choices}

]]> TL68- Translation or Reflection or dilation_MC (R) var board=JXG.JSXGraph.initBoard(BOARDID,{ boundingbox:[-12,12,12,0], axis:false, grid:false, showCopyright:false, showNavigation:false, keepaspectratio:true }); var p0=board.create('point',[{Xa},{Ya}],{fixed:true,size:'0',name:'',showInfobox:false}); var p1=board.create('point',[{Xb},{Yb}],{fixed:true,size:'0',name:'',showInfobox:false}); var p2=board.create('point',[{Xc},{Yc}],{fixed:true,size:'0',name:'',showInfobox:false}); var p3=board.create('point',[{Xd},{Yd}],{fixed:true,size:'0',name:'',showInfobox:false}); var poly1=board.create('polygon',[p0,p1,p2,p3],{strokeColor:'{color1}',fillColor:'{color1}',fillOppacity:.25}); var p4=board.create('point',[{Xa1},{Ya1}],{fixed:true,size:'0',name:'',showInfobox:false}); var p5=board.create('point',[{Xb1},{Yb1}],{fixed:true,size:'0',name:'',showInfobox:false}); var p6=board.create('point',[{Xc1},{Yc1}],{fixed:true,size:'0',name:'',showInfobox:false}); var p7=board.create('point',[{Xd1},{Yd1}],{fixed:true,size:'0',name:'',showInfobox:false}); var poly2=board.create('polygon',[p4,p5,p6,p7],{strokeColor:'{color2}',fillColor:'{color2}',fillOppacity:.25}); ]]> The figure is reflected through the line. It is a reflection.

]]> TL68- Translation or Reflection or dilation_MC (trans) var board=JXG.JSXGraph.initBoard(BOARDID,{ boundingbox:[0,12,12,0], axis:false, grid:false, showCopyright:false, showNavigation:false, keepaspectratio:true }); var p0=board.create('point',[{Xa},{Ya}],{fixed:true,size:'0',name:'',showInfobox:false}); var p1=board.create('point',[{Xb},{Yb}],{fixed:true,size:'0',name:'',showInfobox:false}); var p2=board.create('point',[{Xc},{Yc}],{fixed:true,size:'0',name:'',showInfobox:false}); var p3=board.create('point',[{Xd},{Yd}],{fixed:true,size:'0',name:'',showInfobox:false}); var poly1=board.create('polygon',[p0,p1,p2,p3],{strokeColor:'{color1}',fillColor:'{color1}',fillOppacity:.25}); var p4=board.create('point',[{Xa1},{Ya1}],{fixed:true,size:'0',name:'',showInfobox:false}); var p5=board.create('point',[{Xb1},{Yb1}],{fixed:true,size:'0',name:'',showInfobox:false}); var p6=board.create('point',[{Xc1},{Yc1}],{fixed:true,size:'0',name:'',showInfobox:false}); var p7=board.create('point',[{Xd1},{Yd1}],{fixed:true,size:'0',name:'',showInfobox:false}); var poly2=board.create('polygon',[p4,p5,p6,p7],{strokeColor:'{color2}',fillColor:'{color2}',fillOppacity:.25}); ]]> The {color2} figure is moved to the right, and up. It is a translation.

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. 0,join("",abs(Xt)," to the left"),join("",abs(Xt)," to the right")); yMove=pick(Yt>0,join("",abs(Yt)," down"),join("",abs(Yt)," up")); Xa=Xa1+Xt; Ya=Ya1+Yt; Xb=Xb1+Xt; Yb=Yb1+Yt; Xc=Xc1+Xt; Yc=Yc1+Yt; Xd=Xd1+Xt; Yd=Yd1+Yt; MB=join("","MyBoxH1",bn); s=join("","A:(",Xa,",",Ya,"), B:(",Xb,",",Yb,"), C:(",Xc,",",Yc,"), D:(",Xd,",",Yd,")"); shape=["square","rectangle","trapezoid", "quadrilateral", "parallelogram", "rhombus"]; choices=[shape[randShape[0]],shape[randShape[1]],shape[randShape[2]],shape[randShape[3]],shape[randShape[4]],shape[randShape[5]]]; ans=-1; for (i:[0:6]){ ans=(randShape[i]==correct)?i:ans; } xArray=[Xa,Xb,Xc,Xd,Xa1,Xb1,Xc1,Xd1]; yArray=[Ya,Yb,Yc,Yd,Ya1,Yb1,Yc1,Yd1]; lowX=100; lowY=100; maxX=-1; maxY=-1; for (i:[0:8]){ lowX=(xArray[i]maxX)?i:maxX; maxY=(yArray[i]>maxY)?i:maxY; } maxX=maxX+1; maxY=maxY+1; loxX=lowX-1; lowY=lowY-1; height=((maxY-lowY)*400)/(maxX-lowX); choices=["translation","reflection","dilation"];]]> none 0 1 0 1 0 _err == 0 1 1 What transformation is shown? {_0:choices}

]]> $course$/top/Default for MSII/Test #12/L91- Non Standard Form - Linear Equations/L91- change to Slope Intercept Form L91-Change to Standard form y-mx = b Write the equation in slope-intercept form.
y- $\frac{{mNum}}{{mDen}}$x = {signB} {absB}

]]> y- $\frac{{mNum}}{{mDen}}$x = {signB} {absB} Given +$\frac{{mNum}}{{mDen}}$x +$\frac{{mNum}}{{mDen}}$x Add +$\frac{{mNum}}{{mDen}}$x to both sides y = $\frac{{mNum}}{{mDen}}$x {signB} {absB} The Equation is in Slope-Intercept Form
y=mx+b

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. mA={[1,2],[1,3],[2,3],[1,4],[2,4],[3,4],[1,5],[2,5],[3,5],[1,6],[2,6],[3,6],[4,6],[5,6],[1,7],[2,7],[3,7],[4,7],[5,7],[6,7],[1,8],[2,8],[3,8],[4,8],[5,8],[6,8],[7,8],[1,10],[2,10],[3,10],[4,10],[5,10],[6,10],[7,10],[8,10],[9,10],[2,1],[3,1],[3,2],[4,1],[4,2],[4,3],[5,1],[5,2],[5,3],[6,1],[6,2],[6,3],[6,4]}; b={-7:-1,1:7}; n={-2,3}; m={-3:0,1:4}; bn={1:99999}; 0,"-","+"); absB=abs(b); mNum=mA[0]; mDen=mA[1];]]> none 0 1 0 3 [mNum,mDen,b] 1 1 y= {_0} x + {_2} {_1} ]]> $course$/top/Default for MSII/Test #12/L91- Non Standard Form - Linear Equations/L91- graph the Linear Equation L84 - Graph Equation y- mx =0 (fractional slope) (y-int of 0)

Graph the linear equation y {signOm}$\frac{{DmNum}}{{DmDen}}$x =0 using the slope and y-intercept.

1. Locate the y-intercept. This is the first point.

Since 0 can be added to the equation without changing its value, the y-intercept = 0.

Place the first point at (0,{n}) (The x-value of the y-intercept is always zero.)

2. Use the slope to find a second point.

The slope is {signm}$\frac{{DmNum}}{{DmDen}}$.

First, Start at the y-intercept. Go {mNum} units on the y axis.

{mFB}

Next, go {mDen} on the x-axis. Put your second point at ({mDen},{mNumPb})

]]>

{=-1*n} = {m}x - y

Given

+y +y

Add y to both sides

{=-1*n} +y = {m}x

{n} {n}

Move {=-1*n} to the right side

y = {m}x + {n}

The equation is now in slope-intercept form.

A line can be graphed from two points.

1. Locate the y-intercept. This is the first point.

2. Use the slope to find a second point.

The first point is the y-intercept.

Place the first point at (0,{n}) (The x-value of the y-intercept is always zero.)

The second point is calculated using the slope.

The slope is {m}. Write the slope as a fraction by writing {m} over 1.

slope = $\frac{Δy}{Δx}$ = $\frac{{m}}{1}$

First, Start at the y-intercept. Go {m} units on the y axis.

{mFB}

Next, go 1 unit on the x-axis. Put your second point at (1,{=m+n})

]]> L84 - Graph Equation 0= mx- y (fractional slope) (y-int of 0)

Graph the linear equation {signm}$\frac{{DmNum}}{{DmDen}}$x - y =0 using the slope and y-intercept.

{#A}]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. mA={[1,2],[1,3],[2,3],[1,4],[2,4],[3,4],[1,5],[2,5],[3,5],[1,6],[2,6],[3,6],[4,6],[5,6],[1,7],[2,7],[3,7],[4,7],[5,7],[6,7],[1,8],[2,8],[3,8],[4,8],[5,8],[6,8],[7,8],[1,10],[2,10],[3,10],[4,10],[5,10],[6,10],[7,10],[8,10],[9,10],[2,1],[3,1],[3,2],[4,1],[4,2],[4,3],[5,1],[5,2],[5,3],[6,1],[6,2],[6,3],[6,4]}; b={-7:-1,1:7}; bn={1:99999}; signM={-1,1}; 0,join("","Go down ",abs(mNum)," because the slope is negative"),join("","Go up ",abs(mNum)," because the slope is positive")); signb=pick(b>=0,"-","+"); disb=abs(b); signm=pick(signM>0,"-",""); DmNum=abs(mNum); DmDen=abs(mDen); mNumPb=mNum+b;]]> none 0 #A 1 0 4 [0,b,mDen,mNum+b] ((_1==b+m*_0)*.5) + ((_3==b+m*_2)*.5) 1 1

]]> {signm}$\frac{{DmNum}}{{DmDen}}$x - y =0 Given + y + y Add y to both sides {signm}$\frac{{DmNum}}{{DmDen}}$x = y the equation is in slope-intercept form A line can be graphed from two points.

1. Locate the y-intercept. This is the first point.

Since 0 can be added to the equation without changing its value, the y-intercept = 0.

Place the first point at (0,{n}) (The x-value of the y-intercept is always zero.)

2. Use the slope to find a second point.

The slope is {signm}$\frac{{DmNum}}{{DmDen}}$.

First, Start at the y-intercept. Go {mNum} units on the y axis.

{mFB}

Next, go {mDen} on the x-axis. Put your second point at ({mDen},{mNumPb})

]]> L84 - Graph Equation y-b=mx (fractional slope)

Graph the linear equation y {signDisb} {disb}={signm}$\frac{{DmNum}}{{DmDen}}$x using the slope and y-intercept.

{#A}]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. mA={[1,2],[1,3],[2,3],[1,4],[2,4],[3,4],[1,5],[2,5],[3,5],[1,6],[2,6],[3,6],[4,6],[5,6],[1,7],[2,7],[3,7],[4,7],[5,7],[6,7],[1,8],[2,8],[3,8],[4,8],[5,8],[6,8],[7,8],[1,10],[2,10],[3,10],[4,10],[5,10],[6,10],[7,10],[8,10],[9,10],[2,1],[3,1],[3,2],[4,1],[4,2],[4,3],[5,1],[5,2],[5,3],[6,1],[6,2],[6,3],[6,4]}; b={-7:-1,1:7}; bn={1:99999}; signM={-1,1}; 0,join("","Go down ",abs(mNum)," because the slope is negative"),join("","Go up ",abs(mNum)," because the slope is positive")); signb=pick(b>0,"-","+"); signDisb=pick(b>0,"+","-"); disb=abs(b); signm=pick(signM>0,"-",""); DmNum=abs(mNum); DmDen=abs(mDen); mNumPb=mNum+b;]]> none 0 #A 1 0 4 [0,b,mDen,mNum+b] ((_1==b+m*_0)*.5) + ((_3==b+m*_2)*.5) 1 1

1. Locate the y-intercept. This is the first point.

Place the first point at (0,{n}) (The x-value of the y-intercept is always zero.)

2. Use the slope to find a second point.

The slope is {signm}$\frac{{DmNum}}{{DmDen}}$.

First, Start at the y-intercept. Go {mNum} units on the y axis.

{mFB}

Next, go {mDen} on the x-axis. Put your second point at ({mDen},{mNumPb})

]]> $\frac{y}{{m}}$ = x Given

{m}($\frac{y}{{m}}$) =({m}) x

Multiply both sides by {m} y = {m}x The Equation is in slope-intercept form.

A line can be graphed from two points.

1. Locate the y-intercept. This is the first point.

2. Use the slope to find a second point.

The first point is the y-intercept.

Place the first point at (0,{n}) (The x-value of the y-intercept is always zero.)

The second point is calculated using the slope.

The slope is {m}. Write the slope as a fraction by writing {m} over 1.

slope = $\frac{Δy}{Δx}$ = $\frac{{m}}{1}$

First, Start at the y-intercept. Go {m} units on the y axis.

{mFB}

Next, go 1 unit on the x-axis. Put your second point at (1,{=m+n})

]]> $course$/top/Default for MSII/Test #12/L93- Binary or Base2 Number System L93 - Binary to Decimal (1 to 127) Convert the Binary, or base-2 number, to a decimal number.

]]> 2⁶=64 2⁵=32 2⁴=16 2³=8 2²=4 2¹=2 2⁰=1 {=pick(two6,"0 +","64 +")} {=pick(two5,"0 +","32 +")} {=pick(two4,"0 +","16 +")} {=pick(two3,"0 +","8 +")} {=pick(two2,"0 +","4 +")} {=pick(two1,"0 +","2 +")} {=pick(two0,"0","1 ")} {two6} {two5} {two4} {two3} {two2} {two1} {two0}

The Base-2 Number {two6}{two5}{two4}{two3}{two2}{two1}{two0} is equal to the decimal number {number} because it is the sum of the values.

{=pick(two6,"0 +","64 +")}

{=pick(two5,"0 +","32 +")}

{=pick(two4,"0 +","16 +")}

{=pick(two3,"0 +","8 +")}

{=pick(two2,"0 +","4 +")}

{=pick(two1,"0 +","2 +")}

{=pick(two0,"0","1 ")} = {number}

]]> 1.0000000 0.3333333 0 Your answer is correct. Your answer is partially correct. Your answer is incorrect. number = {1:127:1}; =64)?1:0; number=(number>=64)?number-64:number; #2^5 = 32 Needed to be turned on? two5 = (number>=32)?1:0; number=(number>=32)?number-32:number; #2^4 = 16 Needed to be turned on? two4 = (number>=16)?1:0; number=(number>=16)?number-16:number; #2^3 = 8 Needed to be turned on? two3 = (number>=8)?1:0; number=(number>=8)?number-8:number; #2^2 = 4 Needed to be turned on? two2 = (number>=4)?1:0; number=(number>=4)?number-4:number; #2^1 = 2 Needed to be turned on? two1 = (number>=2)?1:0; number=(number>=2)?number-2:number; #2^0 = 1 Needed to be turned on? two0 = (number>=1)?1:0; number=(number>=1)?number-1:number; ans=two6*1000000+two5*100000+two4*10000+two3*1000+two2*100+two1*10+two0; number=tempNumber;]]> abc 0 1 0 1 number _err == 0 1 1 {ans} = {_0}

]]> L93 - Decimal to Binary (1 to 127) Convert the decimal number {number} to a base-2 number.

The Base-2 Number is {two6}{two5}{two4}{two3}{two2}{two1}{two0} since the values of the digit equal {number}.

{=pick(two6,"0 +","64 +")}

{=pick(two5,"0 +","32 +")}

{=pick(two4,"0 +","16 +")}

{=pick(two3,"0 +","8 +")}

{=pick(two2,"0 +","4 +")}

{=pick(two1,"0 +","2 +")}

{=pick(two0,"0","1 ")} = {number}

y=\(\frac{{mNum}}{{mDen}}\)x + {b}

y=\(\frac{{mNum}}{{mDen}}\)x + {b}

y {signOb} {disb} = \(\frac{{mNum}}{{mDen}}\)x		Given
{signb} {disb} {signb} {disb}		Move {disb} to the right side
y= \(\frac{{mNum}}{{mDen}}\)x {signb} {disb}		The equation is in Slope-Intercept form