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Rotation and Dilation

Rotation and Dilation
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2016-01-20 06:43
CirclePolygonTransformation
This example demonstrates rotation and dilation transformations involving circles and polygons. Using commands like Polygon and Rotate, the construction of transformed shapes is shown. Suitable for middle school and above students learning geometric transformations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, D, E, F) → poly1, a, b, d_1, e, f_1
  2. Rotate(Polygon[Dilate[A, f, C], Dilate[B, f, C], Dilate[D, f, C], Dilate[E, f, C], Dilate[F, f, C]], d, C) → A1
  3. Rotate(Dilate[A1, f, C], d, C) → A2
  4. Rotate(Dilate[A2, f, C], d, C) → A3
  5. Rotate(Dilate[A3, f, C], d, C) → A4
  6. Rotate(Dilate[A4, f, C], d, C) → A5
  7. Rotate(Dilate[A5, f, C], d, C) → A6
  8. Rotate(Dilate[A6, f, C], d, C) → A7
  9. Rotate(Dilate[A7, f, C], d, C) → A8
  10. Rotate(Dilate[A8, f, C], d, C) → A9
  11. Polygon(G, H, I) → poly2, i, g, h
  12. Rotate(Polygon[Dilate[G, f, C], Dilate[H, f, C], Dilate[I, f, C]], d, C) → B1
  13. Rotate(Dilate[B1, f, C], d, C) → B2
  14. Rotate(Dilate[B2, f, C], d, C) → B3
  15. Rotate(Dilate[B3, f, C], d, C) → B4
  16. Rotate(Dilate[B4, f, C], d, C) → B5
  17. Rotate(Dilate[B5, f, C], d, C) → B6
  18. Rotate(Dilate[B6, f, C], d, C) → B7
  19. Rotate(Dilate[B7, f, C], d, C) → B8
  20. Rotate(Dilate[B8, f, C], d, C) → B9
  21. Rotate(Dilate[A9, f, C], d, C) → A10
  22. Rotate(Dilate[A10, f, C], d, C) → A11
  23. Rotate(Dilate[A11, f, C], d, C) → A12
  24. Rotate(Dilate[A12, f, C], d, C) → A13
  25. Rotate(Dilate[A13, f, C], d, C) → A14
  26. Rotate(Dilate[A14, f, C], d, C) → A15
  27. Rotate(Dilate[B9, f, C], d, C) → B10
  28. Rotate(Dilate[B10, f, C], d, C) → B11
  29. Rotate(Dilate[B11, f, C], d, C) → B12
  30. Rotate(Dilate[B12, f, C], d, C) → B13
  31. Rotate(Dilate[B13, f, C], d, C) → B14
  32. Rotate(Dilate[B14, f, C], d, C) → B15

AI Drawing Prompt Reference

Draw a pentagon ABCDE and perform rotation and dilation transformations around point C, with each rotation angle d and dilation factor f. Then, draw a triangle GHI and perform the same transformations around point C. Finally, apply rotation and dilation transformations to the resulting shapes A9 and B9 to generate the final shapes A15 and B15.
The prompt above was compiled from the original drawing commands and is for reference only.