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Rotation Transformation and Polygon Demo

Rotation Transformation and Polygon Demo
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2019-04-03 22:13
PolygonCoordinate GeometryTransformationGeometric Construction
This example demonstrates the dynamic process and geometric properties of polygon rotation around a point. It involves core concepts like rotation transformation, polygon construction, orthogonal lines, and intersection calculations. Constructed using GeoGebra commands such as Point, OrthogonalLine, Polygon, Rotate, Line, Intersect, and If, it visualizes geometric transformations and analytical geometry applications, suitable for high school mathematics education.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. OrthogonalLine(A, xOyPlane) → a
  4. Point(a) → C
  5. OrthogonalLine(C, b) → c
  6. Point(c) → D
  7. Polygon(A, B, D, C) → poli1, a_1, b_1, d, c_1
  8. Rotate(poli1, α, a) → poli1'
  9. Rotate(B, α, a) → B'
  10. Line(B, D) → i
  11. Intersect(a, i) → E
  12. Polygon(E, C, D) → poli2, d_1, e_1, c_2
  13. If(e ≟ true ∨ g ≟ true, Rotate[poli2, α, a]) → poli2'
  14. Polygon(A, F, D, C) → poli3, a_2, f_1, d_2, c_3
  15. If(g ≟ true, Rotate[poli3, α, a]) → poli4
  16. Point(c_1) → G
  17. Polygon(G, A, F, D) → poli5, g_1, a_3, f_2, d_3
  18. If(f ≟ true, Rotate[poli5, α, a]) → poli6