Reflectional Symmetry Demonstration
2013-08-16 14:09
This GeoGebra applet visually demonstrates reflectional (line) symmetry of planar figures. Using the Mirror command and interactive buttons, users can observe the reflection of various image objects across a specific axis of symmetry. The construction incorporates points, segments, lines, and angles to help learners deeply understand the geometric properties of reflection, the determination of the
Loading the GeoGebra board and drawing, please wait…
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.288.0" id="b256d9c1-f080-4851-8f2e-9c24d152869f" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="960" height="660" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.296969696969697" orientation="0" />
<pane location="1" divider="0.10416666666666667" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1" size="400" window="159,134,961,550" />
<view id="1" visible="true" inframe="false" stylebar="false" location="2,1" size="958" window="100,100,600,400" />
<view id="4" toolbar="0 59 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="true" location="1,1" size="300" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 | 1011 || 1008 1009 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="true" location="3" size="221" window="100,100,250,400" />
<view id="16" visible="true" inframe="false" stylebar="false" location="0" size="196" 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" toolbar="0" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="128" visible="false" inframe="true" stylebar="false" location="1" size="480" 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" />
<view id="43" visible="false" inframe="false" stylebar="false" location="1" size="450" window="50,50,500,500" />
<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 , 20 22 21 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="true" stylebar="false" location="1" size="480" window="50,50,500,500" />
</views>
<toolbar show="false" items="0 39 59 | 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 66 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6" position="7" help="false" />
<input show="false" cmd="true" top="false" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="20"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="958" height="454"/>
<coordSystem xZero="605.5" yZero="238.00000000000003" scale="35.006814828331606" yscale="35.00681482833145"/>
<evSettings axes="false" grid="false" 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="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<grid distX="1" distY="1" distTheta="0.5235987755982988"/>
</euclidianView>
<euclidianView>
<viewNumber viewNo="2"/>
<size width="958" height="196"/>
<coordSystem xZero="383.9523077447388" yZero="238.64173488748034" scale="32.747629392105885" yscale="32.747629392106006"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="1" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="175" g="238" b="238"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="10"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<grid distX="1" distY="0.5" distTheta="0.5235987755982988"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="0"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
<angleFromInvTrig val="false"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="image" label="pic1">
<file name="0de44ded35b58b83df1a36bd90cbff85\HKSAR.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-3.8293421778214047" y="-3.8293421778214034" z="1"/>
<startPoint number="1" x="4.170657822178596" y="-3.8293421778214034" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="a ∧ (¬showImage)"/>
<objColor r="0" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<element type="image" label="pic2">
<file name="8af23a4a06fd3b1695f51e838fb94868\Eastern_District_Hong_Kong.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-4" y="-4" z="1"/>
<startPoint number="1" x="4" y="-4" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="b ∧ (¬showImage)"/>
<objColor r="0" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<element type="image" label="pic3">
<file name="59bbf3bcff6ba5f7dd10f7367422d93e\Kwun_Tong_District_logo.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-4" y="-4" z="1"/>
<startPoint number="1" x="4" y="-4" z="1"/>
<startPoint number="2" x="-4" y="3.9619047619047283" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="c ∧ (¬showImage)"/>
<objColor r="0" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<element type="image" label="pic4">
<file name="7165db8fa971a95daa136147e69613bf\Sham_Shui_Po_District_logo.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-3.955854104185652" y="-3.9337811562784792" z="1"/>
<startPoint number="1" x="4.0441458958143475" y="-3.9337811562784792" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="d ∧ (¬showImage)"/>
<objColor r="0" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<element type="image" label="pic5">
<file name="5da28394bd19f4370249b4c67c485964\Shatin_District_logo.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-3.9779270520928267" y="-3.889635260464132" z="1"/>
<startPoint number="1" x="4.022072947907173" y="-3.889635260464132" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="e ∧ (¬showImage)"/>
<objColor r="0" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<element type="image" label="pic6">
<file name="dba09a41e755216805c195f4939ed447\Tsuen_Wan_District_logo.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-4" y="-4" z="1"/>
<startPoint number="1" x="4" y="-4" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="f ∧ (¬showImage)"/>
<objColor r="0" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<element type="image" label="pic7">
<file name="c40759008829375adb1ce483627c5cb4\Tuen_Mun_District.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-4" y="-4" z="1"/>
<startPoint number="1" x="4" y="-4" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="g ∧ (¬showImage)"/>
<objColor r="0" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<element type="image" label="pic8">
<file name="87c3484c1e17fc2ac18e64af6161a923\Wong_Tai_Sin District_logo.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-3.9779270520928263" y="-4.088291791628695" z="1"/>
<startPoint number="1" x="4.022072947907174" y="-4.088291791628695" z="1"/>
<startPoint number="2" x="-3.9779270520928263" y="3.9117082083712713" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="h ∧ (¬showImage)"/>
<objColor r="0" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<element type="image" label="pic9">
<file name="7bd025efea0f16552990c8b201bd5119\Yau_Tsim_Mong_District_logo.png"/>
<inBackground val="false"/>
<startPoint number="0" x="-4" y="-4" z="1"/>
<startPoint number="1" x="4" y="-4" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="i ∧ (¬showImage)"/>
<objColor r="0" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<element type="boolean" label="a">
<value val="true"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="19" y="4"/>
<labelMode val="3"/>
<auxiliary val="true"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="SetValue[b,false] SetValue[c,false] SetValue[d,false] SetValue[e,false] SetValue[f,false] SetValue[g,false] SetValue[h,false] SetValue[i,false] "/>
<caption val="Figure 1"/>
</element>
<element type="boolean" label="b">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="150" y="4"/>
<labelMode val="3"/>
<auxiliary val="true"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="SetValue[a,false] SetValue[c,false] SetValue[d,false] SetValue[e,false] SetValue[f,false] SetValue[g,false] SetValue[h,false] SetValue[i,false] "/>
<caption val="Figure 2"/>
</element>
<element type="boolean" label="c">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="281" y="4"/>
<labelMode val="3"/>
<auxiliary val="true"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="SetValue[a,false] SetValue[b,false] SetValue[d,false] SetValue[e,false] SetValue[f,false] SetValue[g,false] SetValue[h,false] SetValue[i,false] "/>
<caption val="Figure 3"/>
</element>
<element type="boolean" label="d">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="412" y="4"/>
<labelMode val="3"/>
<auxiliary val="true"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="SetValue[a,false] SetValue[b,false] SetValue[c,false] SetValue[e,false] SetValue[f,false] SetValue[g,false] SetValue[h,false] SetValue[i,false] "/>
<caption val="Figure 4"/>
</element>
<element type="boolean" label="e">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="543" y="4"/>
<labelMode val="3"/>
<auxiliary val="true"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="SetValue[a,false] SetValue[b,false] SetValue[c,false] SetValue[d,false] SetValue[f,false] SetValue[g,false] SetValue[h,false] SetValue[i,false] "/>
<caption val="Figure 5"/>
</element>
<element type="boolean" label="f">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="674" y="4"/>
<labelMode val="3"/>
<auxiliary val="true"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="SetValue[a,false] SetValue[b,false] SetValue[c,false] SetValue[d,false] SetValue[e,false] SetValue[g,false] SetValue[h,false] SetValue[i,false] "/>
<caption val="Figure 6"/>
</element>
<element type="boolean" label="g">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="19" y="37"/>
<labelMode val="3"/>
<auxiliary val="true"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="SetValue[a,false] SetValue[b,false] SetValue[c,false] SetValue[d,false] SetValue[e,false] SetValue[f,false] SetValue[h,false] SetValue[i,false] "/>
<caption val="Figure 7"/>
</element>
<element type="boolean" label="h">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="150" y="37"/>
<labelMode val="3"/>
<auxiliary val="true"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="SetValue[a,false] SetValue[b,false] SetValue[c,false] SetValue[d,false] SetValue[e,false] SetValue[f,false] SetValue[g,false] SetValue[i,false] "/>
<caption val="Figure 8"/>
</element>
<element type="boolean" label="i">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="281" y="37"/>
<labelMode val="3"/>
<auxiliary val="true"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="SetValue[a,false] SetValue[b,false] SetValue[c,false] SetValue[d,false] SetValue[e,false] SetValue[f,false] SetValue[g,false] SetValue[h,false] "/>
<caption val="Figure 9"/>
</element>
<element type="point" label="O">
<show object="false" label="false"/>
<objColor r="255" g="127" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="0" y="0" z="1"/>
<pointSize val="4"/>
<pointStyle val="1"/>
</element>
<expression label="select" exp="a ∨ b ∨ c ∨ d ∨ e ∨ f ∨ g ∨ h ∨ i" />
<element type="boolean" label="select">
<value val="true"/>
<show object="false" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label ="A" exp="(0, 5)" type="point"/>
<element type="point" label="A">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="0" y="5" z="1"/>
<pointSize val="4"/>
<pointStyle val="1"/>
</element>
<expression label ="B" exp="(0, -5)" type="point"/>
<element type="point" label="B">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="0" y="-5" z="1"/>
<pointSize val="4"/>
<pointStyle val="1"/>
</element>
<command name="Line">
<input a0="A" a1="B"/>
<output a0="L"/>
</command>
<element type="line" label="L">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelOffset x="-19" y="78"/>
<labelMode val="3"/>
<ggbscript onUpdate="SetValue[P',Mirror[P,L]]"/>
<coords x="10" y="0" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<caption val="反射軸"/>
</element>
<command name="Mirror">
<input a0="pic1" a1="L"/>
<output a0="pic1'"/>
</command>
<element type="image" label="pic1'">
<file name="0de44ded35b58b83df1a36bd90cbff85\HKSAR.png"/>
<inBackground val="false"/>
<startPoint number="0" x="3.829342177821405" y="-3.829342177821403" z="1"/>
<startPoint number="1" x="-4.170657822178595" y="-3.829342177821404" z="1"/>
<startPoint number="2" x="3.8293421778214043" y="4.123320544072054" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="a ∧ showImage"/>
<objColor r="0" g="0" b="0" alpha="0.5"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<command name="Mirror">
<input a0="pic2" a1="L"/>
<output a0="pic2'"/>
</command>
<element type="image" label="pic2'">
<file name="8af23a4a06fd3b1695f51e838fb94868\Eastern_District_Hong_Kong.png"/>
<inBackground val="false"/>
<startPoint number="0" x="4.000000000000001" y="-3.9999999999999996" z="1"/>
<startPoint number="1" x="-3.9999999999999996" y="-4.000000000000001" z="1"/>
<startPoint number="2" x="3.9999999999999996" y="3.999999999999965" z="1"/>
<auxiliary val="false"/>
<show object="false" label="false"/>
<condition showObject="b ∧ showImage"/>
<objColor r="0" g="0" b="0" alpha="0.5"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<command name="Mirror">
<input a0="pic3" a1="L"/>
<output a0="pic3'"/>
</command>
<element type="image" label="pic3'">
<file name="59bbf3bcff6ba5f7dd10f7367422d93e\Kwun_Tong_District_logo.png"/>
<inBackground val="false"/>
<startPoint number="0" x="4.000000000000001" y="-3.9999999999999996" z="1"/>
<startPoint number="1" x="-3.9999999999999996" y="-4.000000000000001" z="1"/>
<startPoint number="2" x="3.9999999999999996" y="3.9619047619047287" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="c ∧ showImage"/>
<objColor r="0" g="0" b="0" alpha="0.5"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<command name="Mirror">
<input a0="pic4" a1="L"/>
<output a0="pic4'"/>
</command>
<element type="image" label="pic4'">
<file name="7165db8fa971a95daa136147e69613bf\Sham_Shui_Po_District_logo.png"/>
<inBackground val="false"/>
<startPoint number="0" x="3.9558541041856525" y="-3.933781156278479" z="1"/>
<startPoint number="1" x="-4.044145895814347" y="-3.9337811562784797" z="1"/>
<startPoint number="2" x="3.9558541041856516" y="3.875742653245296" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="d ∧ showImage"/>
<objColor r="0" g="0" b="0" alpha="0.5"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<command name="Mirror">
<input a0="pic5" a1="L"/>
<output a0="pic5'"/>
</command>
<element type="image" label="pic5'">
<file name="5da28394bd19f4370249b4c67c485964\Shatin_District_logo.png"/>
<inBackground val="false"/>
<startPoint number="0" x="3.977927052092827" y="-3.8896352604641318" z="1"/>
<startPoint number="1" x="-4.022072947907172" y="-3.8896352604641327" z="1"/>
<startPoint number="2" x="3.9779270520928263" y="3.919888549059643" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="e ∧ showImage"/>
<objColor r="0" g="0" b="0" alpha="0.5"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<command name="Mirror">
<input a0="pic6" a1="L"/>
<output a0="pic6'"/>
</command>
<element type="image" label="pic6'">
<file name="dba09a41e755216805c195f4939ed447\Tsuen_Wan_District_logo.png"/>
<inBackground val="false"/>
<startPoint number="0" x="4.000000000000001" y="-3.9999999999999996" z="1"/>
<startPoint number="1" x="-3.9999999999999996" y="-4.000000000000001" z="1"/>
<startPoint number="2" x="3.9999999999999996" y="3.999999999999965" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="f ∧ showImage"/>
<objColor r="0" g="0" b="0" alpha="0.5"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<command name="Mirror">
<input a0="pic7" a1="L"/>
<output a0="pic7'"/>
</command>
<element type="image" label="pic7'">
<file name="c40759008829375adb1ce483627c5cb4\Tuen_Mun_District.png"/>
<inBackground val="false"/>
<startPoint number="0" x="4.000000000000001" y="-3.9999999999999996" z="1"/>
<startPoint number="1" x="-3.9999999999999996" y="-4.000000000000001" z="1"/>
<startPoint number="2" x="3.9999999999999996" y="3.999999999999965" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="g ∧ showImage"/>
<objColor r="0" g="0" b="0" alpha="0.5"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<command name="Mirror">
<input a0="pic8" a1="L"/>
<output a0="pic8'"/>
</command>
<element type="image" label="pic8'">
<file name="87c3484c1e17fc2ac18e64af6161a923\Wong_Tai_Sin District_logo.png"/>
<inBackground val="false"/>
<startPoint number="0" x="3.9779270520928267" y="-4.088291791628694" z="1"/>
<startPoint number="1" x="-4.022072947907173" y="-4.088291791628696" z="1"/>
<startPoint number="2" x="3.977927052092826" y="3.9117082083712718" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="h ∧ showImage"/>
<objColor r="0" g="0" b="0" alpha="0.5"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<command name="Mirror">
<input a0="pic9" a1="L"/>
<output a0="pic9'"/>
</command>
<element type="image" label="pic9'">
<file name="7bd025efea0f16552990c8b201bd5119\Yau_Tsim_Mong_District_logo.png"/>
<inBackground val="false"/>
<startPoint number="0" x="4.000000000000001" y="-3.9999999999999996" z="1"/>
<startPoint number="1" x="-3.9999999999999996" y="-4.000000000000001" z="1"/>
<startPoint number="2" x="3.9999999999999996" y="3.999999999999965" z="1"/>
<auxiliary val="false"/>
<show object="true" label="false"/>
<condition showObject="i ∧ showImage"/>
<objColor r="0" g="0" b="0" alpha="0.5"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
</element>
<element type="button" label="button1">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="0" alpha="255"/>
<layer val="3"/>
<labelOffset x="24" y="91"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[A,(0,5)] SetValue[B,(0,-5)]"/>
<font serif="false" sizeM="2" size="20" style="0"/>
<dimensions width="250" height="40" />
<caption val="Vertical line of reflection"/>
</element>
<element type="button" label="button2">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="0" alpha="255"/>
<layer val="3"/>
<labelOffset x="24" y="140"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[A,(-5,0)] SetValue[B,(5,0)]"/>
<font serif="false" sizeM="2" size="20" style="0"/>
<dimensions width="250" height="40" />
<caption val="Horizontal line of reflection"/>
</element>
<element type="point" label="P">
<show object="true" label="false"/>
<condition showObject="show"/>
<objColor r="51" g="153" b="0" alpha="0"/>
<layer val="3"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<ggbscript onUpdate="SetValue[P',Mirror[P,L]]"/>
<coords x="5" y="5" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Intersect">
<input a0="L" a1="OrthogonalLine[P, L]"/>
<output a0="D"/>
</command>
<element type="point" label="D">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="3"/>
<labelMode val="0"/>
<coords x="0" y="500" z="100"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="P" a1="D"/>
<output a0="j"/>
</command>
<element type="segment" label="j">
<show object="true" label="false"/>
<condition showObject="show"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelMode val="0"/>
<decoration type="2"/>
<selectionAllowed val="false"/>
<coords x="0" y="-5" z="25"/>
<lineStyle thickness="5" type="10" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="point" label="P'">
<show object="true" label="false"/>
<condition showObject="show"/>
<objColor r="51" g="153" b="0" alpha="0"/>
<layer val="3"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<ggbscript onUpdate="SetValue[P,Mirror[P',L]]"/>
<coords x="-5.000000000000001" y="4.999999999999999" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="D" a1="P'"/>
<output a0="k"/>
</command>
<element type="segment" label="k">
<show object="true" label="false"/>
<condition showObject="show"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelMode val="0"/>
<decoration type="2"/>
<selectionAllowed val="false"/>
<coords x="8.881784197001252e-16" y="-5.000000000000001" z="25.000000000000004"/>
<lineStyle thickness="5" type="10" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Angle">
<input a0="L" a1="j"/>
<output a0="α"/>
</command>
<element type="angle" label="α">
<angleStyle val="1"/>
<value val="4.71238898038469"/>
<show object="true" label="false"/>
<condition showObject="show"/>
<objColor r="255" g="0" b="0" alpha="0.25"/>
<layer val="3"/>
<labelMode val="1"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<arcSize val="20"/>
<selectionAllowed val="false"/>
</element>
<element type="boolean" label="show">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelOffset x="346" y="135"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="SetValue[P,(5,5)]"/>
<caption val="Show perpendicular line segments"/>
</element>
<element type="boolean" label="showImage">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelOffset x="346" y="86"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="Show image of reflection"/>
</element>
<element type="button" label="button0">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelOffset x="842" y="9"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[lang,If[lang==1,2,1]] RunClickScript[buttonLang] "/>
<font serif="false" sizeM="1.4" size="8" style="0"/>
<caption val="中文"/>
</element>
<element type="button" label="buttonLang">
<show object="false" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelOffset x="711" y="26"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetCaption[button0,If[lang==1,"ENG","中文"]] SetCaption[a,If[lang==1,"圖案1","Figure 1"]] SetCaption[b,If[lang==1,"圖案2","Figure 2"]] SetCaption[c,If[lang==1,"圖案3","Figure 3"]] SetCaption[d,If[lang==1,"圖案4","Figure 4"]] SetCaption[e,If[lang==1,"圖案5","Figure 5"]] SetCaption[f,If[lang==1,"圖案6","Figure 6"]] SetCaption[g,If[lang==1,"圖案7","Figure 7"]] SetCaption[h,If[lang==1,"圖案8","Figure 8"]] SetCaption[i,If[lang==1,"圖案9","Figure 9"]] SetCaption[button1,If[lang==1,"鉛垂反射軸","Vertical line of reflection"]] SetCaption[button2,If[lang==1,"水平反射軸","Horizontal line of reflection"]] SetCaption[showImage,If[lang==1,"顯示反射影像","Show image of reflection"]] SetCaption[show,If[lang==1,"顯示垂直線段","Show perpendicular line segments"]] "/>
<font serif="false" sizeM="2" size="20" style="0"/>
</element>
<element type="numeric" label="lang">
<value val="2"/>
<symbolic val="true" />
<show object="false" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="3"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
</construction>
</geogebra>