Dilation of Polygon Area Demonstration
2014-11-23 11:07
This GeoGebra example demonstrates the dilation (scaling transformation) of polygons and its effect on area. Using Polygon, Dilate, and Ray commands, it constructs original polygons and their dilated images from a center point, visually illustrating the mathematical relationship between scale factors and area changes. Ideal for teaching geometric transformations, similar figures, and area ratios.
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<objColor r="0" g="0" b="0" alpha="0.0"/>
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<labelMode val="0"/>
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<lineStyle thickness="2" type="15" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Ray">
<input a0="A" a1="B"/>
<output a0="l"/>
</command>
<element type="ray" label="l">
<show object="true" label="false"/>
<condition showObject="q ∨ o"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
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<keepTypeOnTransform val="true"/>
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<command name="Ray">
<input a0="A" a1="H"/>
<output a0="m"/>
</command>
<element type="ray" label="m">
<show object="true" label="false"/>
<condition showObject="q"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
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<lineStyle thickness="2" type="15" typeHidden="1"/>
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<keepTypeOnTransform val="true"/>
</element>
<command name="Ray">
<input a0="A" a1="G"/>
<output a0="n"/>
</command>
<element type="ray" label="n">
<show object="true" label="false"/>
<condition showObject="q"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
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<lineStyle thickness="2" type="15" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Ray">
<input a0="A" a1="F"/>
<output a0="p"/>
</command>
<element type="ray" label="p">
<show object="true" label="false"/>
<condition showObject="q"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
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<lineStyle thickness="2" type="15" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
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<element type="boolean" label="o">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="26" y="86"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="三角形"/>
</element>
<element type="boolean" label="q">
<value val="true"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="118" y="85"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="多邊形"/>
</element>
<expression label="text1" exp=""三角形的面積 ＝" + poly2 + " 放大／縮小 k 倍的三角形面積 ＝" + poly3 + """ />
<element type="text" label="text1">
<show object="true" label="false"/>
<condition showObject="o"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<absoluteScreenLocation x="31" y="176"/>
</element>
<expression label="text2" exp=""多邊形的面積 ＝" + poly1 + " 放大／縮小 k 倍的多邊形面積 ＝" + poly1' + """ />
<element type="text" label="text2">
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<condition showObject="q"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<absoluteScreenLocation x="30" y="247"/>
</element>
</construction>
</geogebra>