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Rectangle Transformation Demo by Mrs. Cole

Rectangle Transformation Demo by Mrs. Cole
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2019-01-22 11:28
Coordinate GeometryTransformationGeometric Construction
This example demonstrates transformations of a rectangle in a plane, such as translation, rotation, and dilation. Key math concepts include geometric transformations, vectors, coordinate geometry, and geometric construction. It utilizes commands like Segment, Slope, OrthogonalLine, Point, Ray, Line, Intersect, Midpoint, Circle, Dilate, Vector, CircleSector, Translate, Rotate, Polygon, and Angle from GeoGebra. Suitable for high school students learning geometric transformations and for classroom demonstrations.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Slope(a) → c
  3. OrthogonalLine(A, a) → e
  4. Point(e) → C
  5. Ray(A, C) → d
  6. Point(d) → D
  7. Segment(A, D) → f
  8. Line(D, a) → g
  9. Line(B, f) → h
  10. Intersect(g, h) → E
  11. Segment(D, E) → i
  12. Segment(E, B) → j
  13. Midpoint(A, E) → F
  14. Circle(A, (0.2 * Min[f, i])) → k
  15. Intersect(k, f) → G,
  16. Intersect(k, a, 1) → H
  17. Dilate(A, If[0 < l ≤ 1, 1 - l, 0], B) → A'
  18. Vector(A, A') → u
  19. CircleSector(A, H, G) → p
  20. Translate(p, u) → p'
  21. Rotate(p', If[1 < l ≤ 2, ((l - 1) * π / 2), 1.5707963267948966], B) → p''
  22. Dilate(B, If[2 < l ≤ 3, 3 - l, 0], E) → B'
  23. Vector(B, B') → v
  24. Translate(p'', v) → p'''
  25. Rotate(p''', If[3 < l ≤ 4, ((l - 3) * π / 2), 1.5707963267948966], E) → q
  26. Dilate(E, If[4 < l ≤ 5, 5 - l, 0], D) → E'
  27. Vector(E, E') → w
  28. Translate(q, w) → q'
  29. Rotate(q', If[5 < l ≤ 6, ((l - 5) * π / 2), 1.5707963267948966], D) → q''
  30. Dilate(D, If[6 < l ≤ 7, 7 - l, 0], F) → D'
  31. Vector(D, D') → m
  32. Segment(D, D') → n
  33. Dilate(F, If[7 < l ≤ 8, 8 - l, 0], B) → F'
  34. Segment(F, F') → r
  35. Dilate(A, If[8 < l ≤ 9, 9 - l, 0], F) → A'_1
  36. Segment(A, A'_1) → s
  37. Dilate(F, If[9 < l ≤ 10, 10 - l, 0], E) → F'_1
  38. Segment(F, F'_1) → t
  39. Polygon(A, B, E, D) → poly1, a_1, b_1, e_1, d_1
  40. Angle(E, F, D) → α
  41. Angle(B, A, F) → γ
  42. Angle(F, A, D) → δ
  43. Rotate(F, If[10 < l ≤ 11, ((l - 10) * α), α], F) → F'_2
  44. Rotate(F'_1, If[10 < l ≤ 11, ((l - 10) * α), α], F) → I
  45. Segment(F'_2, I) → t'
  46. Rotate(F'_2, If[11 < l ≤ 12, ((l - 11) * (π - α)), π - α], F) → J
  47. Rotate(I, If[11 < l ≤ 12, ((l - 11) * (π - α)), π - α], F) → I'
  48. Segment(J, I') → t''
  49. Rotate(J, If[12 < l ≤ 13, ((l - 12) * α), α], F) → J'
  50. Rotate(I', If[12 < l ≤ 13, ((l - 12) * α), α], F) → I''
  51. Segment(J', I'') → t'''
  52. Segment(A, F) → c_1
  53. Intersect(k, c_1) → K,
  54. CircleSector(A, H, K) → f_1
  55. CircleSector(A, K, G) → g_1
  56. Dilate(A, If[16 < l ≤ 17, 17 - l, 0], E) → A'_2
  57. Dilate(A, If[16 < l ≤ 17, 17 - l, 0], B) → A'_3
  58. Dilate(A, If[16 < l ≤ 17, 17 - l, 0], D) → A'_4
  59. Vector(A, A'_3) → u_1
  60. Vector(A, A'_2) → v_1
  61. Vector(A, A'_4) → w_1
  62. Translate(f_1, u_1) → h_1
  63. Translate(f_1, v_1) → k_1
  64. Translate(f_1, w_1) → p_1
  65. Rotate(h_1, If[17 < l ≤ 18, ((l - 17) * (π / 2 + δ)), π / 2 + δ], B) → q_1
  66. Rotate(p_1, If[17 < l ≤ 18, ((l - 17) * ((3 * π / 2) + δ)), (3 * π / 2) + δ], D) → r_1
  67. Rotate(k_1, If[17 < l ≤ 18, ((l - 17) * π), 3.141592653589793], E) → s_1
  68. Dilate(A, If[18 < l ≤ 19, 19 - l, 0], E) → A'_5
  69. Dilate(A, If[18 < l ≤ 19, 19 - l, 0], D) → A'_6
  70. Dilate(A, If[18 < l ≤ 19, 19 - l, 0], B) → A'_7
  71. Vector(A, A'_7) → i_1
  72. Vector(A, A'_5) → j_1
  73. Vector(A, A'_6) → l_1
  74. Translate(g_1, l_1) → t_1
  75. Translate(g_1, j_1) → c_2
  76. Translate(g_1, i_1) → d_2
  77. Rotate(d_2, If[19 < l ≤ 20, ((l - 19) * δ), δ], B) → e_2
  78. Rotate(c_2, If[19 < l ≤ 20, ((-(l - 19)) * π), -3.141592653589793], E) → f_2
  79. Rotate(t_1, If[19 < l ≤ 20, ((l - 19) * (π + δ)), π + δ], D) → g_2