Controllable Coordinate System Construction
2020-05-13 06:04
This GeoGebra example demonstrates constructing a dynamically controllable 2D coordinate system using vectors, intersections, and commands like Sequence and Zip. By defining base points and vectors, it generates axes and grid lines, helping users understand the underlying construction logic and parametric control of coordinate systems in coordinate geometry.
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.579.0" app="classic" platform="d" id="b699a013-f8bf-49e8-a130-72de35d2ac30" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1920" height="1030" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.13020833333333334" 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="390" window="100,100,700,550" />
<view id="1" visible="false" inframe="false" stylebar="true" location="1" size="1636" window="100,100,600,400" />
<view id="2" visible="true" inframe="false" stylebar="true" location="3" size="1891" 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="20"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1636" height="776"/>
<coordSystem xZero="713.6008264462806" yZero="448.5851239669422" scale="54.99999999999997" yscale="55.00000000000006"/>
<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"/>
</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="">
<command name="Intersect">
<input a0="xAxis" a1="yAxis"/>
<output a0="A"/>
</command>
<element type="point" label="A">
<show object="true" label="true" ev="4"/>
<condition showObject="e"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-38" y="47"/>
<labelMode val="3"/>
<coords x="0.0" y="-0.0" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
<caption val="$O$"/>
</element>
<command name="Point">
<input a0="xAxis"/>
<output a0="B"/>
</command>
<element type="point" label="B">
<show object="true" label="false" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-27" y="17"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-0.9200150262960117" y="0.0" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="xAxis"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="true" label="true" ev="4"/>
<condition showObject="e"/>
<objColor r="32" g="32" b="32" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-20" y="44"/>
<labelMode val="3"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="6.934530428249447" y="0.0" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<caption val="$x$"/>
</element>
<command name="Vector">
<input a0="B" a1="C"/>
<output a0="u"/>
</command>
<element type="vector" label="u">
<show object="true" label="false" ev="4"/>
<condition showObject="e"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="7.854545454545459" y="0.0" z="0.0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint exp="B"/>
</element>
<command name="Point">
<input a0="yAxis"/>
<output a0="D"/>
</command>
<element type="point" label="D">
<show object="true" label="false" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-12" y="37"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="0.0" y="-0.6257250187828683" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="yAxis"/>
<output a0="E"/>
</command>
<element type="point" label="E">
<show object="true" label="true" ev="4"/>
<condition showObject="e"/>
<objColor r="32" g="32" b="32" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-31" y="29"/>
<labelMode val="3"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="0.0" y="6.447002253944397" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
<caption val="$y$"/>
</element>
<command name="Vector">
<input a0="D" a1="E"/>
<output a0="v"/>
</command>
<element type="vector" label="v">
<show object="true" label="false" ev="4"/>
<condition showObject="e"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="7.072727272727266" z="0.0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<coordStyle style="cartesian"/>
<startPoint exp="D"/>
</element>
<command name="Div">
<input a0="x(B) + 1" a1="1"/>
<output a0="a"/>
</command>
<element type="numeric" label="a">
<value val="0.0"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="Div">
<input a0="x(C)" a1="1"/>
<output a0="b"/>
</command>
<element type="numeric" label="b">
<value val="6.0"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="Div">
<input a0="y(D) + 1" a1="1"/>
<output a0="c"/>
</command>
<element type="numeric" label="c">
<value val="0.0"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="Div">
<input a0="y(E)" a1="1"/>
<output a0="d"/>
</command>
<element type="numeric" label="d">
<value val="6.0"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="Sequence">
<input a0="(e, d)" a1="e" a2="a" a3="b"/>
<output a0="l1"/>
</command>
<element type="list" label="l1">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="Sequence">
<input a0="(e, c)" a1="e" a2="a" a3="b"/>
<output a0="l2"/>
</command>
<element type="list" label="l2">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="Zip">
<input a0="Segment[M, N]" a1="M" a2="l1" a3="N" a4="l2"/>
<output a0="l3"/>
</command>
<element type="list" label="l3">
<show object="true" label="true" ev="4"/>
<condition showObject="f"/>
<objColor r="192" g="192" b="192" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="3" type="15" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="Sequence">
<input a0="(a, e)" a1="e" a2="c" a3="d"/>
<output a0="l4"/>
</command>
<element type="list" label="l4">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="Sequence">
<input a0="(b, e)" a1="e" a2="c" a3="d"/>
<output a0="l5"/>
</command>
<element type="list" label="l5">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="Zip">
<input a0="Segment[M, N]" a1="M" a2="l4" a3="N" a4="l5"/>
<output a0="l6"/>
</command>
<element type="list" label="l6">
<show object="true" label="true" ev="4"/>
<condition showObject="f"/>
<objColor r="192" g="192" b="192" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="3" type="15" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<element type="boolean" label="f">
<value val="true"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="73" y="110"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="网格"/>
</element>
<element type="boolean" label="e">
<value val="true"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="71" y="69"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="坐标系"/>
</element>
</construction>
</geogebra>