Interactive Geometric Rotation Transformation Demo
2014-03-15 13:45
This example demonstrates rotation transformations in plane geometry. Using interactive sliders to control the rotation angle, it shows the dynamic process of rotating polygons, circles, and rectangles around a specified center point. Users can observe the relationships between corresponding points, sides, and angles before and after rotation, intuitively understanding that rotation is an isometry
In collections
Coordinate Geometry (Secondary 1)
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<show object="false" label="false" ev="4"/>
<condition showObject="showRect ∧ showPoint"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<coords x="0" y="3" z="-12"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Rotate">
<input a0="F" a1="(k * theta)" a2="O"/>
<output a0="F'"/>
</command>
<element type="point" label="F'">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Rotate">
<input a0="G" a1="(k * theta)" a2="O"/>
<output a0="G'"/>
</command>
<element type="point" label="G'">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="E'" a1="F'" a2="O'" a3="G'"/>
<output a0="Rect'" a1="r1'" a2="r2'" a3="r3'" a4="r4'"/>
</command>
<element type="polygon" label="Rect'">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="showRect ∧ showPoint ∧ (k > 0)"/>
<objColor r="255" g="127" b="0" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<element type="segment" label="r1'">
<show object="true" label="false" ev="4"/>
<condition showObject="showRect ∧ showPoint ∧ (k > 0)"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="r2'">
<show object="true" label="false" ev="4"/>
<condition showObject="showRect ∧ showPoint ∧ (k > 0)"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="r3'">
<show object="false" label="false" ev="4"/>
<condition showObject="showRect ∧ showPoint ∧ (k > 0)"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="r4'">
<show object="true" label="false" ev="4"/>
<condition showObject="showRect ∧ showPoint ∧ (k > 0)"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="boolean" label="showRect">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<condition showObject="showPoint"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelOffset x="510" y="10"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="Show hints"/>
</element>
<expression label="input" exp=""P""/>
<element type="text" label="input">
<show object="false" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<startPoint x="-7.500093585577798" y="1.9405328258610672" z="1"/>
</element>
<command name="Textfield">
<input a0="input"/>
<output a0="inputBox1"/>
</command>
<element type="textfield" label="inputBox1">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelOffset x="113" y="11"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript onUpdate="SetCaption[E,If[showAxis,input+" = %v",input]] SetCaption[E',If[showAxis,input+"' = %v",input+"'"]]"/>
<linkedGeo exp="input"/>
<length val="2"/>
<caption val="_"/>
</element>
<element type="boolean" label="showAxis">
<value val="true"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelOffset x="710" y="10"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="ShowAxes[1,showAxis] SetCaption[E,If[showAxis,input+" = %v",input]] SetCaption[E',If[showAxis,input+"' = %v",input+"'"]]"/>
<caption val="Show coordinates"/>
</element>
<element type="button" label="button0">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelOffset x="865" y="65"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[lang,If[lang==1,2,1]] RunClickScript[buttonLang] "/>
<font serif="false" sizeM="1.4" size="10" style="0"/>
<caption val="中文"/>
</element>
<element type="button" label="buttonLang">
<show object="false" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelOffset x="974" y="59"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetCaption[button0,If[lang==1,"ENG","中文"]] SetCaption[showPoint,If[lang==1,"點","Point"]] SetCaption[showPic,If[lang==1,"三角形ABC","Triangle ABC"]] SetCaption[showRect,If[lang==1,"顯示提示","Show hints"]] SetCaption[showAxis,If[lang==1,"顯示坐標","Show coordinates"]] SetCaption[showImage,If[lang==1,"顯示旋轉影像","Show image"]] "/>
<font serif="false" sizeM="2" size="24" style="0"/>
</element>
<expression label="text1" exp=""" + (If[lang ≟ 1, "繞O點：", "Rotate about point O:"]) + """ />
<element type="text" label="text1">
<show object="true" label="false" ev="11"/>
<condition showObject="showPoint ∨ showPic"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<absoluteScreenLocation x="218" y="38"/>
</element>
</construction>
</geogebra>