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Animation 81: Polygon Transformation

Animation 81: Polygon Transformation
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2016-06-27 11:50
PolygonVectorTransformation
This example demonstrates the transformation process of a polygon. Key mathematical concepts include geometric transformations, vectors, and polygons. Using GeoGebra commands such as Rotate, Dilate, and Translate, it shows the rotation, scaling, and translation of a polygon. Suitable for high school geometry and transformation lessons.

GeoGebra Commands & Parameters

  1. Line(A, B) → a_4
  2. Slope(a_4) → b_3
  3. Intersect(a_4, x = 0) → C_1
  4. PointIn(d_4) → C
  5. Segment(A, C) → b
  6. Segment(B, C) → a
  7. Segment(A, B) → g
  8. Polygon(A, B, C) → poly1, d_1, a_1, b_1
  9. Angle(A, C, B) → α
  10. Rotate(A, α / 2, C) → A'
  11. Angle(A, C, A') → β
  12. Ray(C, A') → h
  13. Intersect(h, g) → D
  14. Dilate(C, If[0 < i ≤ 1, 1 - i, 0], D) → D'
  15. Segment(C, D') → j
  16. Circle(C, (0.2 * j)) → k
  17. Intersect(k, b) → F, K
  18. Intersect(k, j) → G,
  19. CircleSector(C, F, G) → p
  20. Rotate(p, If[1.5 < i ≤ 2.5, ((i - 1.5) * β), β], C) → p'
  21. Segment(A, D) → c_1
  22. Segment(D, B) → c_2
  23. Ray(A, C) → n
  24. Line(B, j) → q
  25. Intersect(q, n) → E
  26. Dilate(C, If[3 < i ≤ 4, 4 - i, 0], B) → D'_1
  27. Vector(C, D'_1) → u
  28. Translate(p', u) → p''
  29. Rotate(p'', If[4 < i ≤ 5, (((i - 4) * 180))°, 180°], B) → p'''
  30. Dilate(B, If[5 < i ≤ 6, 6 - i, 0], E) → B'
  31. Dilate(C, If[5 < i ≤ 6, 6 - i, 0], E) → D'_2
  32. Segment(B, B') → r
  33. Segment(C, D'_2) → d
  34. Polygon(A, D, C) → poly2, d_2, a_2, e_1
  35. Polygon(D, B, C) → poly3, d_3, e_2, b_2
  36. Dilate(D, If[7 < i, 8 - i, 0], B) → E'
  37. Dilate(C, If[7 < i, 8 - i, 0], E) → D'_3
  38. Polygon(A, E', D'_3) → poly4, d'_3, a_3, e'
  39. Dilate(B, If[6 < i ≤ 7, 7 - i, 0], E) → B'_1
  40. Vector(B, B'_1) → v
  41. Translate(p''', v) → t
  42. Line(E, a) → c_3
  43. Circle(E, 1) → f_1
  44. Intersect(f_1, c_3, 2) → I
  45. Intersect(f_1, r, 1) → J
  46. Angle(I, E, J) → γ
  47. Rotate(t, If[7 < i ≤ 8, ((i - 7) * γ), γ], E) → t'
  48. Segment(A, B) → e