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Rectangle Transformation Demo by Dan Dale

Rectangle Transformation Demo by Dan Dale
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2019-06-27 04:31
PolygonVectorCoordinate GeometryTransformationGeometric Construction
This example illustrates geometric transformations of rectangles, such as translation, rotation, and dilation, without specific lengths or angle measures. Key math concepts include transformation geometry, central symmetry, centroid, and vector operations. GeoGebra commands like Segment, Vector, Translate, Rotate, and Dilate are used in construction. Suitable for high school mathematics classes to visually understand transformational and spatial geometry concepts.

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

AI Drawing Prompt Reference

Draw a rectangle with one horizontal side and one slanted side from an endpoint. Inside, draw a segment from the midpoint of the horizontal side to the opposite slanted side, marking their intersection. Center a small arc at this intersection, intersecting both sides, then translate and rotate this arc sequentially along the rectangle's boundary to create moving sectors. Also draw several dynamic segments between vertices showing shrinking or expanding motion, and label three key angles to illustrate rotation and symmetry transformations.
The prompt above was compiled from the original drawing commands and is for reference only.