Introduction to Rectangular Coordinates
2015-01-17 10:13
This GeoGebra applet introduces the fundamental concepts of the rectangular coordinate system. Users can explore point locations, axes, quadrant divisions, and related polygon and vector representations. Featuring bilingual support, it helps beginners visually understand the 2D coordinate plane and basic geometric figures, serving as a great introduction to coordinate geometry.
In collections
Secondary 1 Coordinate Geometry
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<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="270" 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"/>
<selectionAllowed val="false"/>
<lineStyle thickness="9" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</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>
<command name="DynamicCoordinates">
<input a0="Q'" a1="round((10 * x(Q'))) / 10" a2="round((10 * y(Q'))) / 10"/>
<output a0="Q"/>
</command>
<element type="point" label="Q">
<show object="true" label="false" ev="4"/>
<condition showObject="showQ"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="8"/>
<labelOffset x="5" y="37"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="-9" y="-2" z="1"/>
<pointSize val="6"/>
<pointStyle val="0"/>
<caption val="%n%v"/>
</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>
<expression label="text2" exp=""Q" + Q + """ />
<element type="text" label="text2">
<show object="true" label="false" ev="20"/>
<condition showObject="showQ"/>
<objColor r="0" 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="Q"/>
<labelOffset x="4" y="36"/>
</element>
<element type="boolean" label="showQ">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelOffset x="847" y="12"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="SetValue(Q,(0,0))"/>
<caption val="Q"/>
</element>
<expression label="text1" exp=""" + (If[show1 ∨ showQ, "P" + P, "P"]) + """ />
<element type="text" label="text1">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="1.4" size="10" style="0"/>
<startPoint exp="P"/>
<labelOffset x="9" y="28"/>
</element>
</construction>
</geogebra>