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Rotating a Polygon Around a Point with Slider Control

Rotating a Polygon Around a Point with Slider Control
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2014-03-04 00:32
PolygonAngleTransformationGeometric ConstructionSlider Animation
① This example demonstrates a polygon (formed by points A, B, C, D, E, F) rotating around a fixed point G, with a slider α controlling the rotation angle in real time, showing the original and rotated shapes simultaneously. ② The core mathematical concept is rotation transformation in plane geometry, involving the center of rotation, angle of rotation, correspondence of points and sides, and the invariant properties of shape and size under rotation. ③ Construction details: The GeoGebra commands Polygon and Rotate are used to create the original polygon poly1 and its rotated image poly1', along with the sides (a, b, c, d, e, f and their primed versions). The slider α adjusts the rotation angle, and point G serves as the rotation center. ④ Suitable for middle or high school students to understand rotation transformations, and useful for dynamic geometry demonstrations or math lab activities to enhance spatial reasoning and transformation thinking.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D, E, F) → poly1, a, b, c, d, e, f
  2. Rotate(A, (-α), G) → A'
  3. Rotate(B, (-α), G) → B'
  4. Rotate(C, (-α), G) → C'
  5. Rotate(D, (-α), G) → D'
  6. Rotate(E, (-α), G) → E'
  7. Rotate(F, (-α), G) → F'
  8. Polygon(A', B', C', D', E', F') → poly1', a', b', c', d', e', f'

AI Drawing Prompt Reference

Draw a hexagon with six vertices and rotate it around a fixed point. Show both the original and rotated hexagons simultaneously, using different colors or line styles to distinguish them. Add a slider control to adjust the rotation angle in real time, with counterclockwise rotation. Clearly mark the rotation center point. Ensure the rotated shape has the same size and shape as the original, differing only in position and orientation. Construct by first drawing the original hexagon, then rotating each vertex around the center by the slider angle, and finally connecting the rotated vertices to form the new hexagon.
The prompt above was compiled from the original drawing commands and is for reference only.