Exercise: Counterclockwise Rotation of a Triangle
2015-07-07 06:49
This exercise demonstrates the counterclockwise rotation of a triangle. Using the Rotate command, users can observe the triangle's position change around a center point. It includes coordinate inputs and angle controls, helping learners understand rotational transformation properties like shape preservation and angle relationships. Ideal for interactive geometry practice.
Loading the GeoGebra board and drawing, please wait…
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.42.0" id="af239683-f90d-4411-b4b7-f9f1536b9480" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1341" height="753" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.14914243102162567" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1,1" size="400" window="131,77,1120,597" />
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 | 551 550 11 , 22 , 23 , 55 56 57 , 12 | 69 | 510 511 , 512 513 | 533 531 , 534 532 , 522 523 , 537 536 , 535 | 521 520 | 36 , 38 49 560 | 571 30 29 570 31 33 | 17 | 540 40 41 42 , 27 28 35 , 6 , 502" visible="false" inframe="false" stylebar="false" location="1,1,1" size="500" window="100,100,600,400" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="false" location="1,1" size="300" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="true" location="1" size="1330" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="false" location="3" size="200" window="100,100,250,400" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
</views>
<toolbar show="true" items="0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="true" cmd="true" top="false" />
<dockBar show="true" east="true" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="12"/>
<graphicsSettings javaLatexFonts="false"/>
</gui>
<euclidianView>
<size width="1330" height="616"/>
<coordSystem xZero="711.6694816118455" yZero="399.8639565634659" scale="32.54115975600269" yscale="32.54115975600271"/>
<evSettings axes="true" grid="true" gridIsBold="false" pointCapturing="0" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="10"/>
<axis id="0" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true" tickDistance="1.0"/>
<axis id="1" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true" tickDistance="1.0"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0"/>
<coordStyle val="0"/>
<angleFromInvTrig val="false"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="練習 - 逆時針旋轉（三角形）" author="" date="">
<element type="numeric" label="t">
<value val="2.0"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="w">
<value val="-4.0"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="v">
<value val="1.0"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="u">
<value val="-2.0"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="button" label="button1">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="1152" y="36"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="G=Random[1,4] SetValue[u,If[G==1 || G==4,Random[1,3],Random[-1,-3]]] SetValue[v,If[G==1 || G==2,Random[1,3],Random[-1,-3]]] SetValue[w,If[G==1 || G==4,Random[4,6],Random[-4,-6]]] SetValue[t,If[G==1 || G==2,Random[1,3],Random[-1,-3]]] SetValue[q,If[G==1 || G==4,Random[4,6],Random[-4,-6]]] SetValue[r,If[G==1 || G==2,Random[4,6],Random[-4,-6]]] A=(u,v) B=(w,t) C=(q,r) H=Random[1,3] SetValue(α,0+H*90°) SetValue(inputxA,0) SetValue(inputxB,0) SetValue(inputxC,0) SetValue(inputyA,0) SetValue(inputyB,0) SetValue(inputyC,0)"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<caption val="Try Again"/>
</element>
<expression label="A" exp="(u, v)" type="point" />
<element type="point" label="A">
<show object="true" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-16" y="-4"/>
<labelMode val="0"/>
<coords x="-2.0" y="1.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="B" exp="(w, t)" type="point" />
<element type="point" label="B">
<show object="true" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-4.0" y="2.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="numeric" label="a_2">
<value val="1.0"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="angle" label="α">
<angleStyle val="3"/>
<value val="4.71238898038469"/>
<slider min="0*°" max="270*°" absoluteScreenLocation="true" width="180.0" x="822.0" y="122.0" fixed="true" horizontal="true"/>
<show object="false" label="true"/>
<objColor r="0" g="100" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<lineStyle thickness="10" type="0" typeHidden="2"/>
<arcSize val="30"/>
<animation step="90*°" speed="1" type="0" playing="false"/>
</element>
<expression label="text1" exp=""Input the reflection point of the image (A', B' and C') and press “Enter”.""/>
<element type="text" label="text1">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<absoluteScreenLocation x="76" y="149"/>
</element>
<element type="numeric" label="inputxA">
<value val="0.0"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="inputxB">
<value val="0.0"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="inputyA">
<value val="0.0"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="inputyB">
<value val="0.0"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<command name="Random">
<input a0="1" a1="4"/>
<output a0="G"/>
</command>
<element type="numeric" label="G">
<value val="2.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="Intersect">
<input a0="xAxis" a1="yAxis"/>
<output a0="I"/>
</command>
<element type="point" label="I">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="-0.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Random">
<input a0="1" a1="3"/>
<output a0="H"/>
</command>
<element type="numeric" label="H">
<value val="3.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<element type="numeric" label="q">
<value val="-4.0"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="r">
<value val="4.0"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<expression label="C" exp="(q, r)" type="point" />
<element type="point" label="C">
<show object="true" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-4.0" y="4.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="A" a1="B" a2="C"/>
<output a0="poly1" a1="c" a2="a" a3="b"/>
</command>
<element type="polygon" label="poly1">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="c">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="-1.0" y="-2.0" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="a">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="-2.0" y="0.0" z="-8.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="b">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="3.0" y="2.0" z="4.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Rotate">
<input a0="A" a1="α" a2="I"/>
<output a0="A'"/>
</command>
<element type="point" label="A'">
<show object="true" label="true"/>
<condition showObject="inputxA ≟ AnswerxA ∧ inputyA ≟ AnsweryA"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.0000000000000004" y="1.9999999999999998" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Rotate">
<input a0="B" a1="α" a2="I"/>
<output a0="B'"/>
</command>
<element type="point" label="B'">
<show object="false" label="true"/>
<condition showObject="inputxB ≟ AnswerxB ∧ inputyB ≟ AnsweryB"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="7" y="18"/>
<labelMode val="0"/>
<coords x="2.000000000000001" y="3.9999999999999996" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Rotate">
<input a0="C" a1="α" a2="I"/>
<output a0="C'"/>
</command>
<element type="point" label="C'">
<show object="true" label="true"/>
<condition showObject="inputxC ≟ AnswerxC ∧ inputyC ≟ AnsweryC"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="4.000000000000001" y="3.999999999999999" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="A'" a1="B'" a2="C'"/>
<output a0="poly1'" a1="c'" a2="a'" a3="b'"/>
</command>
<element type="polygon" label="poly1'">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<condition showObject="inputxA ≟ AnswerxA ∧ inputyA ≟ AnsweryA ∧ inputxB ≟ AnswerxB ∧ inputyB ≟ AnsweryB ∧ inputxC ≟ AnswerxC ∧ inputyC ≟ AnsweryC"/>
<objColor r="0" g="0" b="255" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="c'">
<show object="true" label="false"/>
<condition showObject="inputxA ≟ AnswerxA ∧ inputyA ≟ AnsweryA ∧ inputxB ≟ AnswerxB ∧ inputyB ≟ AnsweryB ∧ inputxC ≟ AnswerxC ∧ inputyC ≟ AnsweryC"/>
<objColor r="0" g="0" b="255" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="-1.9999999999999998" y="1.0000000000000004" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="a'">
<show object="true" label="false"/>
<condition showObject="inputxA ≟ AnswerxA ∧ inputyA ≟ AnsweryA ∧ inputxB ≟ AnswerxB ∧ inputyB ≟ AnsweryB ∧ inputxC ≟ AnswerxC ∧ inputyC ≟ AnsweryC"/>
<objColor r="0" g="0" b="255" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="4.440892098500626E-16" y="2.0" z="-7.999999999999998"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="b'">
<show object="true" label="false"/>
<condition showObject="inputxA ≟ AnswerxA ∧ inputyA ≟ AnsweryA ∧ inputxB ≟ AnswerxB ∧ inputyB ≟ AnsweryB ∧ inputxC ≟ AnswerxC ∧ inputyC ≟ AnsweryC"/>
<objColor r="0" g="0" b="255" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="1.9999999999999993" y="-3.0000000000000004" z="3.999999999999999"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Textfield">
<input a0="inputxA"/>
<output a0="inputBox1"/>
</command>
<element type="textfield" label="inputBox1">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelOffset x="79" y="173"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<linkedGeo exp="inputxA"/>
<length val="2"/>
<caption val="A' = ("/>
</element>
<command name="Textfield">
<input a0="inputyA"/>
<output a0="inputBox2"/>
</command>
<element type="textfield" label="inputBox2">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="201" y="173"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<linkedGeo exp="inputyA"/>
<length val="2"/>
<caption val=","/>
</element>
<expression label="text3" exp="")""/>
<element type="text" label="text3">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<absoluteScreenLocation x="270" y="200"/>
</element>
<command name="Textfield">
<input a0="inputxA"/>
<output a0="inputBox1_1"/>
</command>
<element type="textfield" label="inputBox1_1">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="79" y="173"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<linkedGeo exp="inputxA"/>
<length val="2"/>
<caption val="A' = ("/>
</element>
<command name="Textfield">
<input a0="inputxA"/>
<output a0="inputBox1_2"/>
</command>
<element type="textfield" label="inputBox1_2">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="79" y="173"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<linkedGeo exp="inputxA"/>
<length val="2"/>
<caption val="A' = ("/>
</element>
<command name="Textfield">
<input a0="inputxB"/>
<output a0="inputBox3"/>
</command>
<element type="textfield" label="inputBox3">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="81" y="223"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<linkedGeo exp="inputxB"/>
<length val="2"/>
<caption val="B' = ("/>
</element>
<command name="Textfield">
<input a0="inputyB"/>
<output a0="inputBox4"/>
</command>
<element type="textfield" label="inputBox4">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="201" y="223"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<linkedGeo exp="inputyB"/>
<length val="2"/>
<caption val=","/>
</element>
<expression label="text3_1" exp="")""/>
<element type="text" label="text3_1">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<absoluteScreenLocation x="270" y="249"/>
</element>
<element type="numeric" label="inputxC">
<value val="0.0"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="inputyC">
<value val="0.0"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<command name="Textfield">
<input a0="inputxC"/>
<output a0="inputBox5"/>
</command>
<element type="textfield" label="inputBox5">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="78" y="273"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<linkedGeo exp="inputxC"/>
<length val="2"/>
<caption val="C' = ("/>
</element>
<command name="Textfield">
<input a0="inputyC"/>
<output a0="inputBox6"/>
</command>
<element type="textfield" label="inputBox6">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="202" y="274"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<linkedGeo exp="inputyC"/>
<length val="2"/>
<caption val=","/>
</element>
<expression label="text3_2" exp="")""/>
<element type="text" label="text3_2">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<absoluteScreenLocation x="270" y="300"/>
</element>
<expression label="AnswerxA" exp="x(A')" />
<element type="numeric" label="AnswerxA">
<value val="1.0000000000000004"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="AnswerxB" exp="x(B')" />
<element type="numeric" label="AnswerxB">
<value val="2.000000000000001"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="AnswerxC" exp="x(C')" />
<element type="numeric" label="AnswerxC">
<value val="4.000000000000001"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="AnsweryA" exp="y(A')" />
<element type="numeric" label="AnsweryA">
<value val="1.9999999999999998"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="AnsweryB" exp="y(B')" />
<element type="numeric" label="AnsweryB">
<value val="3.9999999999999996"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="AnsweryC" exp="y(C')" />
<element type="numeric" label="AnsweryC">
<value val="3.999999999999999"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="text4" exp=""Good Job!""/>
<element type="text" label="text4">
<show object="true" label="true"/>
<condition showObject="inputxA ≟ AnswerxA ∧ inputyA ≟ AnsweryA ∧ inputxB ≟ AnswerxB ∧ inputyB ≟ AnsweryB ∧ inputxC ≟ AnswerxC ∧ inputyC ≟ AnsweryC"/>
<objColor r="0" g="153" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="4.0" size="36" style="3"/>
<absoluteScreenLocation x="808" y="77"/>
</element>
<expression label="text2" exp=""Where is the refection of the image after it rotates " + α + " counter clockwise through origin O?"" />
<element type="text" label="text2">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="1"/>
<absoluteScreenLocation x="38" y="56"/>
</element>
</construction>
</geogebra>