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Rotation Animation of Quadrilateral Transformation

Rotation Animation of Quadrilateral Transformation
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2017-02-10 07:22
PolygonTransformationGeometric Construction
This example demonstrates the rotation transformation of a quadrilateral. Key mathematical concepts include rotation, angle, line, and polygon. Using GeoGebra commands such as Rotate, Angle, Line, and Polygon, the rotation process of the quadrilateral is dynamically shown. Suitable for students at junior high school level and above to learn geometric transformations.

GeoGebra Commands & Parameters

  1. Rotate(B, a°, A) → B'
  2. Angle(B, A, B') → α
  3. Ray(A, B) → f
  4. Ray(A, B') → g
  5. Line(B, g) → h
  6. Point(g) → C
  7. Line(C, f) → i
  8. Intersect(h, i) → D
  9. Segment(C, D) → j
  10. Segment(A, B) → k
  11. Segment(B, D) → l
  12. Segment(A, C) → m
  13. Min(m, k) → b
  14. Circle(C, (0.2 * b)) → d
  15. Circle(A, (0.2 * b)) → e
  16. Circle(B, (0.2 * b)) → p
  17. Circle(D, (0.2 * b)) → c
  18. Intersect(e, k, 1) → E
  19. Intersect(e, m, 1) → F
  20. Intersect(p, k, 1) → G
  21. Intersect(p, l, 1) → H
  22. Intersect(d, g, 2) → I
  23. Ray(C, I) → q
  24. Intersect(c, h, 2) → J
  25. Ray(D, J) → r
  26. Intersect(c, i, 2) → K
  27. Ray(D, K) → s
  28. Dilate(B, If[0 < o ≤ 1, 1 - o, 0], A) → A'
  29. Rotate(E, If[1 < o ≤ 2, ((o - 1) * α), α], A) → E'
  30. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], C) → A'_1
  31. Vector(A, A'_1) → u
  32. Segment(A, A'_1) → f_1
  33. Dilate(C, If[2 < o ≤ 3, 3 - o, 0], D) → C'
  34. Vector(C, C') → v
  35. Dilate(B, If[3 < o ≤ 4, 4 - o, 0], D) → D'
  36. Polygon(A, B, D, C) → poly1, a_1, b_1, d_2, c_2
  37. Dilate(A, If[5.5 < o ≤ 6.5, 6.5 - o, 0], C) → A'_2
  38. Vector(A, A'_2) → w
  39. Translate(A, w) → A'_3
  40. Translate(A', w) → A''
  41. Dilate(A, If[6.5 < o ≤ 7.5, 7.5 - o, 0], B) → A'_4
  42. Vector(A, A'_4) → u_1
  43. Translate(A, u_1) → A'_5
  44. Translate(A'_1, u_1) → L
  45. Intersect(d, i) → M, N
  46. Intersect(d, g) → O, P
  47. Angle(A, C, N) → β
  48. Rotate(N, If[6.5 < o ≤ 7.5, ((-(o - 6.5)) * β), (-β)], C) → N'
  49. Dilate(C, If[7.5 < o ≤ 8.5, 8.5 - o, 0], B) → C'_1
  50. Vector(C, C'_1) → v_1
  51. Line(A, B) → p_1
  52. Intersect(e, p_1) → T, U
  53. Ray(A, T) → q_1
  54. Intersect(e, f_1) → V,
  55. Intersect(d, i, 1) → W
  56. Ray(C, W) → r_1
  57. Segment(B, A') → t
  58. Rotate(V, If[2 < o ≤ 3, ((o - 2) * (π - α)), π - α], A) → V'
  59. CircleSector(A, V, V') → c_1
  60. Dilate(A, If[12 < o ≤ 13, 13 - o, 0], C) → A'_8
  61. Vector(A, A'_8) → w_1
  62. Dilate(C, If[13 < o ≤ 14, 14 - o, 0], D) → C'_2
  63. Vector(C, C'_2) → e_1
  64. Dilate(A, If[3 < o ≤ 4, 4 - o, 0], C) → A'_9
  65. Vector(A, A'_9) → g_1
  66. Translate(B, g_1) → B'_3
  67. Translate(A', g_1) → A''_1
  68. Segment(B'_3, A''_1) → t'
  69. Segment(B, D') → h_1
  70. Dilate(A, If[4 < o ≤ 5, 5 - o, 0], C) → A'_6
  71. Vector(A, A'_6) → d_1
  72. Translate(c_1, d_1) → k_1
  73. Dilate(C, If[6 < o ≤ 7, 7 - o, 0], D) → C'_3
  74. Vector(C, C'_3) → i_1
  75. Translate(k_1, i_1) → s_1