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Projection, Rotation, Dilation, and Reflection

Projection, Rotation, Dilation, and Reflection
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2016-07-22 04:33
Coordinate GeometryTransformationGeometric Construction
This example demonstrates geometric transformations such as projection, rotation, dilation, and reflection of a triangle. Key math concepts include transformations, geometric properties of triangles, and coordinate geometry. It uses commands like Polygon, Intersect, Rotate, Dilate, and Mirror in GeoGebra. Suitable for high school students learning geometric transformations to understand their mathematical essence and practical applications.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Intersect(xAxis, yAxis) → O
  3. Rotate(A, α, O) → A'
  4. Rotate(B, α, O) → B'
  5. Rotate(C, α, O) → C'
  6. Polygon(A', B', C') → poly1', c', a', b'
  7. Rotate(A, (-β), O) → A'_1
  8. Rotate(B, (-β), O) → B'_1
  9. Rotate(C, (-β), O) → C'_1
  10. Polygon(A'_1, B'_1, C'_1) → poly1'_1, c'_1, a'_1, b'_1
  11. Dilate(A, f) → A'_2
  12. Dilate(B, f) → B'_2
  13. Dilate(C, f) → C'_2
  14. Polygon(A'_2, B'_2, C'_2) → poly1'_2, c'_2, a'_2, b'_2
  15. Mirror(A, x = 0) → A'_3
  16. Mirror(B, x = 0) → B'_3
  17. Mirror(C, x = 0) → C'_3
  18. Polygon(A'_3, B'_3, C'_3) → poly1'_3, c'_3, a'_3, b'_3
  19. Mirror(A, y = 0) → A'_4
  20. Mirror(B, y = 0) → B'_4
  21. Mirror(C, y = 0) → C'_4
  22. Polygon(A'_4, B'_4, C'_4) → poly1'_4, c'_4, a'_4, b'_4
  23. Mirror(A'_4, x = 0) → D
  24. Mirror(B'_4, x = 0) → E
  25. Mirror(C'_4, x = 0) → F
  26. Polygon(D, E, F) → poly2, f_1, d_1, e_1