动点最值与椭圆旋转模型探究
2020-07-22 10:51
本范例演示了基于椭圆模型的动点最值问题与几何旋转变换。通过构建椭圆及其相关几何元素，利用旋转命令探究动点在特定条件下的轨迹与极值情况。结合多边形、圆、角及线段等基础几何构造，直观展示圆锥曲线中的最值优化问题，帮助深入理解解析几何中的动点轨迹与旋转变换的内在联系。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.553.0" app="classic" platform="d" id="62fb3a90-13a0-4432-b3d7-876d14c597a3" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1920" height="1040" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.109375" 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 , 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="4097" visible="false" inframe="false" stylebar="true" location="1,1" size="194" window="100,100,700,550" />
<view id="1" visible="true" inframe="false" stylebar="false" location="1" size="1678" window="100,100,600,400" />
<view id="2" visible="true" inframe="false" stylebar="true" location="3" size="210" window="100,100,600,400" />
<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" toolbar="0" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
</views>
<toolbar show="true" items="0 39 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="true" cmd="true" top="algebra" />
<dockBar show="true" east="true" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="12"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1678" height="872"/>
<coordSystem xZero="565.4993259368596" yZero="262.177411315584" scale="43.908702659396454" yscale="43.908702659396425"/>
<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>
<algebraView>
<mode val="3"/>
</algebraView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="1" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2.0" max="2.0" step="1.0"/>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="point" label="B">
<show object="true" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-5.0" y="-3.0" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="point" label="C">
<show object="true" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="3.0" y="-3.0" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="B" a1="C" a2="3"/>
<output a0="poly1" a1="f" a2="g" a3="h" a4="A"/>
</command>
<element type="polygon" label="poly1">
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="102" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="f">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="102" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="0.0" y="8.0" z="24.0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="g">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="102" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="-6.9282032302755105" y="-3.9999999999999982" z="8.784609690826535"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="h">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="102" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="6.9282032302755105" y="-4.000000000000002" z="22.641016151377542"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="point" label="A">
<show object="true" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="-0.9999999999999982" y="3.92820323027551" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="OrthogonalLine">
<input a0="A" a1="f"/>
<output a0="k"/>
</command>
<element type="line" label="k">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-8.0" y="0.0" z="-7.999999999999986"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="Circle">
<input a0="A" a1="B" a2="C"/>
<output a0="c"/>
</command>
<element type="conic" label="c">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="-19.856406460551025" A3="0.0" A4="1.0" A5="0.6905989232414963"/>
<eqnStyle style="specific"/>
</element>
<command name="LineBisector">
<input a0="h"/>
<output a0="i"/>
</command>
<element type="line" label="i">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="4.000000000000002" y="6.9282032302755105" z="8.784609690826525"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="Intersect">
<input a0="k" a1="i"/>
<output a0="D"/>
</command>
<element type="point" label="D">
<show object="true" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-55.425625842203985" y="-38.27687752661224" z="55.425625842204084"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="D" a1="B"/>
<output a0="j"/>
</command>
<element type="segment" label="j">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.309401076758503" y="-4.000000000000002" z="-0.45299461620749115"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="D" a1="C"/>
<output a0="l"/>
</command>
<element type="segment" label="l">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.309401076758503" y="3.9999999999999982" z="5.071796769724486"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Angle">
<input a0="B" a1="D" a2="C"/>
<output a0="α"/>
</command>
<element type="angle" label="α">
<angleStyle val="0"/>
<value val="2.0943951023931957"/>
<show object="true" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="3"/>
<lineStyle thickness="5" type="0" typeHidden="2" opacity="178"/>
<arcSize val="15"/>
</element>
<element type="numeric" label="a">
<value val="12.9"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="3"/>
<slider min="10" max="16" absoluteScreenLocation="true" width="200.0" x="116.0" y="150.0" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<caption val="BP+CP"/>
</element>
<element type="numeric" label="b">
<value val="4.62"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="3"/>
<slider min="0" max="12" absoluteScreenLocation="true" width="200.0" x="117.0" y="292.0" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.01" speed="1" type="0" playing="false"/>
<caption val="BP"/>
</element>
<command name="Circle">
<input a0="B" a1="b"/>
<output a0="d"/>
</command>
<element type="conic" label="d">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="12.6556" A3="0.0" A4="5.0" A5="3.0"/>
<eqnStyle style="specific"/>
</element>
<command name="Circle">
<input a0="C" a1="a - b"/>
<output a0="e"/>
</command>
<element type="conic" label="e">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="-50.55840000000002" A3="0.0" A4="-3.0" A5="3.0"/>
<eqnStyle style="specific"/>
</element>
<command name="Intersect">
<input a0="d" a1="e" a2="2"/>
<output a0="P"/>
</command>
<element type="point" label="P">
<show object="true" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-27" y="30"/>
<labelMode val="0"/>
<coords x="-3.9508750000000012" y="-7.499304027777519" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="P" a1="B"/>
<output a0="p"/>
</command>
<element type="segment" label="p">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-4.499304027777519" y="-1.0491249999999988" z="-25.643895138887594"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="P" a1="C"/>
<output a0="q"/>
</command>
<element type="segment" label="q">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="2"/>
<coords x="-4.499304027777519" y="6.950875000000002" z="34.35053708333256"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="P" a1="D"/>
<output a0="r"/>
</command>
<element type="segment" label="r">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="1"/>
<coords x="-6.808705104536022" y="2.950875000000003" z="-4.770834006915755"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Angle">
<input a0="C" a1="P" a2="B"/>
<output a0="β"/>
</command>
<element type="angle" label="β">
<angleStyle val="0"/>
<value val="1.225402971913255"/>
<show object="true" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelOffset x="-4" y="-28"/>
<labelMode val="2"/>
<lineStyle thickness="5" type="0" typeHidden="2" opacity="178"/>
<arcSize val="30"/>
</element>
<command name="Line">
<input a0="B" a1="D"/>
<output a0="m"/>
</command>
<element type="line" label="m">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-2.309401076758503" y="4.000000000000002" z="0.45299461620749115"/>
<lineStyle thickness="5" type="15" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="Line">
<input a0="D" a1="C"/>
<output a0="n"/>
</command>
<element type="line" label="n">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.309401076758503" y="3.9999999999999982" z="5.071796769724486"/>
<lineStyle thickness="5" type="15" typeHidden="1" opacity="178"/>
<eqnStyle style="implicit"/>
</element>
<command name="Circle">
<input a0="B" a1="D" a2="C"/>
<output a0="s"/>
</command>
<element type="conic" label="s">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="7.856406460551021" A3="0.0" A4="0.9999999999999997" A5="5.309401076758504"/>
<eqnStyle style="specific"/>
</element>
<command name="Ellipse">
<input a0="B" a1="C" a2="P"/>
<output a0="t"/>
</command>
<element type="conic" label="t">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="409.64000000000044" A1="665.6400000000004" A2="-10641.648100000028" A3="0.0" A4="409.64000000000044" A5="1996.9200000000014"/>
<eqnStyle style="implicit"/>
</element>
<command name="Rotate">
<input a0="P" a1="120°" a2="D"/>
<output a0="P'"/>
</command>
<element type="point" label="P'">
<show object="true" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="6.37194908740498" y="0.15822091563410445" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="D" a1="P'"/>
<output a0="f_1"/>
</command>
<element type="segment" label="f_1">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.8488198388756016" y="7.371949087404978" z="4.242240263077416"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="P" a1="P'"/>
<output a0="g_1"/>
</command>
<element type="segment" label="g_1">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-7.657524943411624" y="10.322824087404982" z="47.16007239591356"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Angle">
<input a0="P" a1="D" a2="P'"/>
<output a0="γ"/>
</command>
<element type="angle" label="γ">
<angleStyle val="0"/>
<value val="2.0943951023931957"/>
<show object="true" label="true"/>
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<lineStyle thickness="5" type="0" typeHidden="2" opacity="178"/>
<arcSize val="30"/>
</element>
<command name="Polygon">
<input a0="D" a1="B" a2="P"/>
<output a0="t1" a1="p_1" a2="d_1" a3="b_1"/>
</command>
<element type="polygon" label="t1">
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="p_1">
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="2.309401076758503" y="-4.000000000000002" z="-0.45299461620749115"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="d_1">
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="4.499304027777519" y="1.0491249999999988" z="25.643895138887594"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="b_1">
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="-6.808705104536022" y="2.950875000000003" z="-4.770834006915755"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="D" a1="C" a2="P'"/>
<output a0="t2" a1="p'" a2="d_2" a3="c_1"/>
</command>
<element type="polygon" label="t2">
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="p'">
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="2.309401076758503" y="3.9999999999999982" z="5.071796769724486"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="d_2">
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="-3.1582209156341046" y="3.37194908740498" z="19.590510009117256"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="c_1">
<show object="true" label="false" ev="4"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="0.8488198388756016" y="-7.371949087404978" z="-4.242240263077416"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="point" label="E">
<show object="false" label="false"/>
<objColor r="77" g="77" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="7.145523667527394" y="-4.00427655647872" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="point" label="F">
<show object="false" label="false"/>
<objColor r="77" g="77" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="18.276574470628443" y="-4.118149198965689" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="image" label="pic1">
<file name="2408c4d15504887822ee72db18aeb402/transferImage.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="E"/>
<startPoint number="1" exp="F"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
</construction>
</geogebra>