直角坐标系入门交互演示
2020-07-25 02:59
本范例演示直角坐标系（笛卡尔坐标系）的基本概念，涵盖坐标轴、象限划分、点的坐标表示及向量。通过DynamicCoordinates与Point命令实现交互式操作，用户可拖动点P观察其横纵坐标(P_x, P_y)的实时变化，并借助多边形(poly1~poly4)直观展示四个象限区域。支持中英文双语切换，适合初学者理解解析几何中坐标、向量与象限的关系。
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<expression label="textQuadrantEng" exp=""P lies in quadrant " + (If[x(P) > 0, If[y(P) > 0, "1", "4"], If[y(P) > 0, "2", "3"]]) + "."" />
<element type="text" label="textQuadrantEng">
<show object="true" label="false" ev="11"/>
<condition showObject="x(P) ≠ 0 ∧ y(P) ≠ 0 ∧ show2 ∧ lang ≠ 1"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<absoluteScreenLocation x="480" y="81"/>
</element>
<expression label="textX" exp=""" + (If[lang ≟ 1, "x坐標是", "x-coordinate is"]) + " " + (x(P)) + """ />
<element type="text" label="textX">
<show object="true" label="false" ev="4"/>
<condition showObject="show1"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="1" size="0" style="1"/>
<startPoint exp="P_x"/>
<labelOffset x="-45" y="31"/>
</element>
<expression label="textXY" exp=""P點的坐標是 " + P + "。"" />
<element type="text" label="textXY">
<show object="true" label="false" ev="11"/>
<condition showObject="show1 ∧ lang ≟ 1"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="1.4" size="10" style="0"/>
<absoluteScreenLocation x="41" y="87"/>
</element>
<expression label="textXYeng" exp=""The coordinates of P are " + P + "."" />
<element type="text" label="textXYeng">
<show object="true" label="false" ev="11"/>
<condition showObject="show1 ∧ lang ≠ 1"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<absoluteScreenLocation x="20" y="81"/>
</element>
<expression label="textY" exp=""" + (If[lang ≟ 1, "y坐標是", "y-coordinate is"]) + " " + (y(P)) + """ />
<element type="text" label="textY">
<show object="true" label="false" ev="4"/>
<condition showObject="show1"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="1" size="0" style="1"/>
<startPoint exp="P_y"/>
<labelOffset x="6" y="-9"/>
</element>
<command name="Vector">
<input a0="P" a1="P_y"/>
<output a0="h"/>
</command>
<element type="vector" label="h">
<show object="true" label="false" ev="4"/>
<condition showObject="show1"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="-4" y="0" z="0"/>
<lineStyle thickness="7" type="15" typeHidden="1"/>
<coordStyle style="cartesian"/>
<startPoint exp="P"/>
</element>
<command name="Vector">
<input a0="P" a1="P_x"/>
<output a0="v"/>
</command>
<element type="vector" label="v">
<show object="true" label="false" ev="4"/>
<condition showObject="show1"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="0" y="-3" z="0"/>
<lineStyle thickness="7" type="15" typeHidden="1"/>
<coordStyle style="cartesian"/>
<startPoint exp="P"/>
</element>
<element type="numeric" label="P2">
<value val="NaN"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="3"/>
<labelMode val="2"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
</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="153" b="153" alpha="255"/>
<layer val="3"/>
<labelOffset x="812" y="12"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetVisibleInView(u_1,1,true) SetVisibleInView(u_2,1,true) SetVisibleInView(textAniX,1,true) SetVisibleInView(textAniY,1,true) SetValue(t,0) StartAnimation(t)"/>
<font serif="false" sizeM="2" size="24" style="0"/>
<dimensions width="118" height="39" />
<caption val="Animate"/>
</element>
<element type="numeric" label="t">
<value val="1"/>
<symbolic val="true" />
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="3"/>
<labelMode val="1"/>
<slider min="0" max="1" absoluteScreenLocation="true" width="200" x="30" y="50" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.001" speed="6" type="3" playing="false"/>
</element>
<expression label="L_1" exp="{Segment[(0, 0), (x(P), 0)], Segment[(x(P), 0), P]}" />
<element type="list" label="L_1">
<show object="false" label="false"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="3"/>
<labelMode val="0"/>
<lineStyle thickness="9" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Point">
<input a0="L_1" a1="t"/>
<output a0="A"/>
</command>
<element type="point" label="A">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="4" y="3" z="1"/>
<pointSize val="6"/>
<pointStyle val="0"/>
</element>
<command name="Vector">
<input a0="(0, 0)" a1="If[y(A) ≟ 0, A, (x(P), 0)]"/>
<output a0="u_1"/>
</command>
<element type="vector" label="u_1">
<show object="true" label="false" ev="9"/>
<objColor r="255" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="4" y="0" z="0"/>
<lineStyle thickness="11" type="0" typeHidden="1" opacity="127"/>
<coordStyle style="cartesian"/>
<startPoint x="0" y="0" z="1"/>
</element>
<command name="Vector">
<input a0="If[y(A) ≟ 0, A, (x(P), 0)]" a1="A"/>
<output a0="u_2"/>
</command>
<element type="vector" label="u_2">
<show object="true" label="false" ev="5"/>
<objColor r="255" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="0" y="3" z="0"/>
<lineStyle thickness="11" type="0" typeHidden="1" opacity="127"/>
<coordStyle style="cartesian"/>
<startPoint x="4" y="0" z="1"/>
</element>
<expression label="Pos1" exp="(x(P) / 2, 0)" type="point" />
<element type="point" label="Pos1">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="8"/>
<labelOffset x="-14" y="46"/>
<labelMode val="0"/>
<coords x="2" y="0" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="Pos2" exp="(x(P), y(P) / 2)" type="point" />
<element type="point" label="Pos2">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="8"/>
<labelMode val="0"/>
<coords x="4" y="1.5" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="textAniX" exp=""" + (x(P)) + """ />
<element type="text" label="textAniX">
<show object="true" label="true" ev="41"/>
<condition showObject="t ≟ 1 ∧ x(P) ≠ 0"/>
<objColor r="255" g="0" b="255" alpha="0"/>
<layer val="8"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="1.4" size="10" style="0"/>
<startPoint exp="Pos1"/>
<labelOffset x="-11" y="36"/>
</element>
<expression label="textAniY" exp=""" + (y(P)) + """ />
<element type="text" label="textAniY">
<show object="true" label="true" ev="41"/>
<condition showObject="t ≟ 1 ∧ y(P) ≠ 0"/>
<objColor r="255" g="0" b="255" alpha="0"/>
<layer val="8"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="1.4" size="10" style="0"/>
<startPoint exp="Pos2"/>
<labelOffset x="7" y="12"/>
</element>
</construction>
</geogebra>