Geometric Demonstration of Convex Lens Imaging
2020-09-24 03:52
This GeoGebra applet dynamically demonstrates convex lens imaging using geometric tools. By defining the principal axis, optical center, and focal points, it traces specific light rays using Ray, OrthogonalLine, and Intersect commands to find the image position. It visually illustrates imaging rules as object distance changes, ideal for physics and geometry teaching.
Loading the GeoGebra board and drawing, please wait…
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.605.0" app="classic" platform="w" id="0485507B-41F3-4D97-8460-09B469E529B9" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="759" height="468" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.997364953886693" orientation="1" />
</panes>
<views>
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 51 | 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="false" stylebar="false" location="1,1,1" size="500" window="100,100,600,400" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 || 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 || 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="false" location="3" size="380" tab="ALGEBRA" window="100,100,600,400" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="300" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="300" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="false" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="128" visible="false" inframe="false" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="4097" visible="false" inframe="false" stylebar="true" location="1" size="408" window="100,100,700,550" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="900" window="50,50,500,500" />
<view id="1" visible="true" inframe="false" stylebar="true" location="" size="466" window="100,100,600,400" />
</views>
<toolbar show="false" items="0 73 62 | 1 501 67 , 5 19 , 72 75 76 | 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 14 68 | 30 29 54 32 31 33 | 25 17 26 60 52 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="false" cmd="true" top="false" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="16"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="756" height="465"/>
<coordSystem xZero="375.25459300037306" yZero="302.8534287007082" scale="54.15104007002089" yscale="54.151040070021025"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="3"/>
<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="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="3" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="numeric" label="a">
<value val="-2"/>
<show object="true" label="false"/>
<objColor r="51" g="255" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="-2.5" max="-2" absoluteScreenLocation="true" width="200" x="181" y="86" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.5" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="b">
<value val="-3.5"/>
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="-6" max="-1" absoluteScreenLocation="true" width="200" x="182" y="147" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.5" speed="1" type="0" playing="false"/>
</element>
<expression label="f" exp="y = 1" type="line"/>
<element type="line" label="f">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0" y="1" z="-1"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="user"/>
</element>
<expression label="F" exp="(a, 0)" type="point" />
<element type="point" label="F">
<show object="true" label="false"/>
<objColor r="51" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-6" y="-2"/>
<labelMode val="0"/>
<coords x="-2" y="0" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<expression label="F_1" exp="((-a), 0)" type="point" />
<element type="point" label="F_1">
<show object="true" label="false"/>
<objColor r="51" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-6" y="-9"/>
<labelMode val="0"/>
<coords x="2" y="0" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<expression label="C" exp="((2 * a), 0)" type="point" />
<element type="point" label="C">
<show object="true" label="false"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelOffset x="-7" y="-4"/>
<labelMode val="0"/>
<coords x="-4" y="0" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<expression label="D" exp="((-2 * a), 0)" type="point" />
<element type="point" label="D">
<show object="true" label="false"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="4" y="0" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<expression label="E" exp="(b, 0)" type="point" />
<element type="point" label="E">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-3.5" y="0" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="OrthogonalLine">
<input a0="E" a1="f"/>
<output a0="g"/>
</command>
<element type="line" label="g">
<show object="false" label="true"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1" y="0" z="-3.5"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="Intersect">
<input a0="f" a1="g"/>
<output a0="F_2"/>
</command>
<element type="point" label="F_2">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-3.5" y="1" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Vector">
<input a0="E" a1="F_2"/>
<output a0="u"/>
</command>
<element type="vector" label="u">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="1" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint exp="E"/>
</element>
<command name="Intersect">
<input a0="f" a1="yAxis"/>
<output a0="G"/>
</command>
<element type="point" label="G">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="1" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Ray">
<input a0="G" a1="F_1"/>
<output a0="h"/>
</command>
<element type="ray" label="h">
<show object="true" label="false"/>
<objColor r="255" g="215" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1" y="2" z="-2"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Intersect">
<input a0="xAxis" a1="yAxis"/>
<output a0="H"/>
</command>
<element type="point" label="H">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="0" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Ray">
<input a0="F_2" a1="H"/>
<output a0="i"/>
</command>
<element type="ray" label="i">
<show object="true" label="false"/>
<objColor r="255" g="215" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1" y="3.5" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="explicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Intersect">
<input a0="h" a1="i"/>
<output a0="I"/>
</command>
<element type="point" label="I">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="7" y="-2" z="1.5"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="OrthogonalLine">
<input a0="I" a1="f"/>
<output a0="j"/>
</command>
<element type="line" label="j">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.5" y="0" z="7"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="Intersect">
<input a0="j" a1="xAxis"/>
<output a0="J"/>
</command>
<element type="point" label="J">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="7" y="0" z="1.5"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Vector">
<input a0="J" a1="I"/>
<output a0="v"/>
</command>
<element type="vector" label="v">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="-1.3333333333333333" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint exp="J"/>
</element>
<command name="Ray">
<input a0="H" a1="F_2"/>
<output a0="k"/>
</command>
<element type="ray" label="k">
<show object="false" label="true"/>
<objColor r="255" g="215" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1" y="-3.5" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Ray">
<input a0="F_1" a1="G"/>
<output a0="l"/>
</command>
<element type="ray" label="l">
<show object="false" label="true"/>
<objColor r="255" g="215" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1" y="-2" z="2"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Intersect">
<input a0="k" a1="l"/>
<output a0="K"/>
</command>
<element type="point" label="K">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Ray">
<input a0="F_2" a1="K"/>
<output a0="m"/>
</command>
<element type="ray" label="m">
<show object="true" label="false"/>
<objColor r="255" g="215" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="5" type="10" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Ray">
<input a0="G" a1="K"/>
<output a0="n"/>
</command>
<element type="ray" label="n">
<show object="true" label="false"/>
<objColor r="255" g="215" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="5" type="10" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="OrthogonalLine">
<input a0="K" a1="f"/>
<output a0="p"/>
</command>
<element type="line" label="p">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="Intersect">
<input a0="p" a1="xAxis"/>
<output a0="L"/>
</command>
<element type="point" label="L">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Vector">
<input a0="L" a1="K"/>
<output a0="w"/>
</command>
<element type="vector" label="w">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="5" type="10" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint exp="L"/>
</element>
<command name="Vector">
<input a0="F_2" a1="G"/>
<output a0="c"/>
</command>
<element type="vector" label="c">
<show object="true" label="false"/>
<objColor r="255" g="215" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3.5" y="0" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint exp="F_2"/>
</element>
<element type="point" label="A">
<show object="false" label="true"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="6" y="0" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="yAxis"/>
<output a0="B"/>
</command>
<element type="point" label="B">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="0" y="-2" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="A" a1="B"/>
<output a0="d"/>
</command>
<element type="conic" label="d">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-4.000000000000007" A3="0" A4="-6" A5="0"/>
<eqnStyle style="specific"/>
</element>
<command name="Point">
<input a0="xAxis"/>
<output a0="M"/>
</command>
<element type="point" label="M">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-6" y="0" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="M" a1="B"/>
<output a0="e"/>
</command>
<element type="conic" label="e">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-4.000000000000007" A3="0" A4="6" A5="0"/>
<eqnStyle style="specific"/>
</element>
<command name="Intersect">
<input a0="d" a1="e" a2="2"/>
<output a0="N"/>
</command>
<element type="point" label="N">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="2.0000000000000018" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="CircleArc">
<input a0="M" a1="N" a2="B"/>
<output a0="q"/>
</command>
<element type="conicpart" label="q">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-4.000000000000007" A3="0" A4="6" A5="0"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="CircleArc">
<input a0="A" a1="N" a2="B"/>
<output a0="r"/>
</command>
<element type="conicpart" label="r">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-4.000000000000007" A3="0" A4="-6" A5="0"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="CircleArc">
<input a0="M" a1="B" a2="N"/>
<output a0="s"/>
</command>
<element type="conicpart" label="s">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-4.000000000000007" A3="0" A4="6" A5="0"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="xAxis"/>
<output a0="O"/>
</command>
<element type="point" label="O">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-6" y="0" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="xAxis"/>
<output a0="P"/>
</command>
<element type="point" label="P">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="6" y="0" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="O" a1="P"/>
<output a0="t"/>
</command>
<element type="segment" label="t">
<show object="true" label="false"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="12" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="text1" exp=""凸透鏡""/>
<element type="text" label="text1">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<startPoint x="-0.4187790344151618" y="-2.3887097382908564" z="1"/>
</element>
<expression label="text2" exp=""焦距""/>
<element type="text" label="text2">
<show object="true" label="true" ev="40"/>
<objColor r="51" g="255" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<absoluteScreenLocation x="32" y="89"/>
</element>
<expression label="text3" exp=""物體距凸透鏡距離""/>
<element type="text" label="text3">
<show object="true" label="true" ev="40"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<absoluteScreenLocation x="29" y="148"/>
</element>
<expression label="text4" exp=""請更改凸透鏡的焦距,以及物體距凸透鏡的距離""/>
<element type="text" label="text4">
<show object="true" label="false" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<absoluteScreenLocation x="30" y="41"/>
</element>
<element type="point" label="Q">
<show object="false" label="false"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="5" y="-2" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="t"/>
<output a0="R"/>
</command>
<element type="point" label="R">
<show object="false" label="false"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="5" y="0" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="Q" a1="R"/>
<output a0="f_1"/>
</command>
<element type="segment" label="f_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-2" y="0" z="10"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Intersect">
<input a0="t" a1="f_1"/>
<output a0="S"/>
</command>
<element type="point" label="S">
<show object="false" label="false"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="120" y="0" z="24"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="t"/>
<output a0="U"/>
</command>
<element type="point" label="U">
<show object="true" label="false"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="4.66741555975306" y="0" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="h_1" exp="y = -2" type="line"/>
<element type="line" label="h_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0" y="1" z="2"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="user"/>
</element>
<command name="OrthogonalLine">
<input a0="U" a1="h_1"/>
<output a0="i_1"/>
</command>
<element type="line" label="i_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1" y="0" z="4.66741555975306"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="Intersect">
<input a0="h_1" a1="i_1"/>
<output a0="V"/>
</command>
<element type="point" label="V">
<show object="false" label="false"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="4.66741555975306" y="-2" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="U" a1="V"/>
<output a0="j_1"/>
</command>
<element type="segment" label="j_1">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2" y="0" z="-9.33483111950612"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="text5" exp=""紙屏擺放""/>
<element type="text" label="text5">
<show object="true" label="false" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<absoluteScreenLocation x="604" y="275"/>
</element>
</construction>
</geogebra>