Exploration of Heterogeneous Speed Translation on Polyline with Two Moving Point
2020-06-29 05:33
This GeoGebra example demonstrates the heterogeneous speed translation problem of two moving points on a polyline. Through the construction of polygons, points, and lines, it illustrates the motion trajectories and geometric relationships of moving points at different speeds. It is suitable for studying translation transformations, moving point loci, and polygon properties in plane geometry, aidin
In collections
Minority Pi GeoGebra Collection
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.591.0" app="classic" platform="d" id="0bee7f93-d445-4207-ad69-caf7f143b1cb" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1936" height="1056" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.13068181818181818" orientation="1" />
<pane location="1" divider="0.6978305785123967" 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 , 538 | 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="1" visible="true" inframe="false" stylebar="true" location="1,3" size="1351" 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="true" inframe="false" stylebar="true" location="1,1" size="306" window="100,100,700,550" />
<view id="2" visible="true" inframe="false" stylebar="true" location="3" size="253" window="100,100,250,400" />
<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="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="900" 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="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="20"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1351" height="811"/>
<coordSystem xZero="344.99999999999994" yZero="417.9999999999999" scale="49.99999999999998" yscale="49.99999999999998"/>
<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="1"/>
<auxiliary show="true"/>
</algebraView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" 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="">
<expression label="A" exp="(0, 0)" type="point"/>
<element type="point" label="A">
<show object="true" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-24" y="30"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<ggbscript val=""/>
<ggbscript onUpdate=""/>
<coords x="0.0" y="0.0" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="B" exp="A + (0, (2 * sqrt(3)))" type="point" />
<element type="point" label="B">
<show object="true" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-19" y="-1"/>
<labelMode val="0"/>
<ggbscript val=""/>
<ggbscript onUpdate=""/>
<coords x="0.0" y="3.4641016151377544" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<expression label="O" exp="A + (2, 0)" type="point" />
<element type="point" label="O">
<show object="true" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-4" y="29"/>
<labelMode val="0"/>
<ggbscript val=""/>
<ggbscript onUpdate=""/>
<coords x="2.0" y="0.0" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<expression label="C" exp="A + (4, (2 * sqrt(3)))" type="point" />
<element type="point" label="C">
<show object="true" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<ggbscript val=""/>
<ggbscript onUpdate=""/>
<coords x="4.0" y="3.4641016151377544" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="A" a1="B" a2="C" a3="O"/>
<output a0="q1" a1="a" a2="b" a3="c" a4="o"/>
</command>
<element type="polygon" label="q1">
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<ggbscript val=""/>
<ggbscript onUpdate=""/>
</element>
<element type="segment" label="a">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="-3.4641016151377544" y="0.0" z="0.0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="b">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<ggbscript val=""/>
<ggbscript onUpdate=""/>
<coords x="0.0" y="4.0" z="-13.856406460551018"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="c">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="3.4641016151377544" y="-2.0" z="-6.928203230275509"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="o">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="0.0" y="-2.0" z="0.0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="l1" exp="{Segment[O, B], Segment[B, C]}" />
<element type="list" label="l1">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<ggbscript val=""/>
<ggbscript onUpdate=""/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<expression label="l2" exp="{Segment[O, C], Segment[C, B]}" />
<element type="list" label="l2">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<ggbscript val=""/>
<ggbscript onUpdate=""/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<element type="numeric" label="d">
<value val="0.16"/>
<show object="true" label="true"/>
<objColor r="255" g="0" b="0" alpha="1.0"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="0.6" absoluteScreenLocation="true" width="200.0" x="345.0" y="154.0" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.01" speed="1" type="0" playing="false"/>
<ggbscript onUpdate=""/>
</element>
<command name="Point">
<input a0="l1" a1="d"/>
<output a0="D"/>
</command>
<element type="point" label="D">
<show object="true" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-26" y="22"/>
<labelMode val="3"/>
<ggbscript val=""/>
<ggbscript onUpdate=""/>
<coords x="1.3599999999999999" y="1.1085125168440815" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<caption val="N"/>
</element>
<command name="Point">
<input a0="l2" a1="(1.5 * d)"/>
<output a0="E"/>
</command>
<element type="point" label="E">
<show object="true" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="4" y="20"/>
<labelMode val="3"/>
<ggbscript val=""/>
<ggbscript onUpdate=""/>
<coords x="2.96" y="1.662768775266122" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<caption val="M"/>
</element>
<command name="Polygon">
<input a0="O" a1="D" a2="E"/>
<output a0="t1" a1="e" a2="o_1" a3="d_1"/>
</command>
<element type="polygon" label="t1">
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.30000001192092896"/>
<layer val="0"/>
<labelMode val="0"/>
<ggbscript val=""/>
<ggbscript onUpdate=""/>
</element>
<element type="segment" label="e">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="-1.1085125168440815" y="-0.6400000000000001" z="2.217025033688163"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="o_1">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="-0.5542562584220405" y="1.6" z="-1.0198315154965552"/>
<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="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="1.662768775266122" y="-0.96" z="-3.325537550532244"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
</construction>
</geogebra>