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Rhombus Transformation Animation

Rhombus Transformation Animation
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2016-06-18 09:24
PolygonTransformationGeometric Construction
In collections Congruence (CO) Cluster Congruence (Vol 2) CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2
This example demonstrates a rhombus transformation animation, involving concepts such as the properties of a rhombus, symmetry, and transformation operations. Using GeoGebra commands like Mirror, Dilate, and Rotate, the animation dynamically shows the changes in a rhombus under different transformations. Suitable for middle school and above students or teachers for geometry education.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Ray(A, B) → b
  3. Point(b) → C
  4. Midpoint(A, C) → D
  5. Line(A, C) → c
  6. Slope(c) → d
  7. OrthogonalLine(D, c) → g
  8. Point(g) → E
  9. Ray(D, E) → h
  10. Point(h) → F
  11. Slope(h) → i
  12. Line(F, c) → l
  13. Point(l) → G
  14. Point(l) → H
  15. Ray(F, G) → m
  16. Ray(F, H) → n
  17. Point(m) → I
  18. Mirror(I, h) → I'
  19. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], C) → A'
  20. Segment(A, A') → p
  21. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], I) → A'_1
  22. Segment(A, A'_1) → q
  23. Segment(A, C) → r
  24. Segment(C, I') → s
  25. Segment(I', I) → t
  26. Segment(I, A) → a_1
  27. Circle(A, (0.2 * Min[a_1, r])) → c_1
  28. Circle(I, (0.2 * Min[a_1, r])) → d_1
  29. Intersect(d_1, a_1, 1) → J
  30. Intersect(d_1, t, 1) → K
  31. Intersect(c_1, r, 1) → L
  32. Intersect(c_1, a_1, 1) → M
  33. Dilate(I, If[2 < o ≤ 3, 3 - o, 0], I') → I'_1
  34. Segment(I, I'_1) → b_1
  35. Dilate(A, If[3 < o ≤ 4, 4 - o, 0], C) → A'_2
  36. Vector(A, A'_2) → u
  37. Translate(A, u) → A'_3
  38. Translate(A'_1, u) → N
  39. Segment(A'_3, N) → q'
  40. OrthogonalLine(A, r) → g_1
  41. Point(g_1) → O
  42. Angle(I, A, O) → α
  43. Angle(I', C, A) → β
  44. Rotate(A'_3, If[4 < o ≤ 5, (((o - 4) * 2) * α), (2 * α)], C) → P
  45. Rotate(N, If[4 < o ≤ 5, (((o - 4) * 2) * α), (2 * α)], C) → N'
  46. Segment(P, N') → q''
  47. Dilate(A, If[5 < o ≤ 6, 6 - o, 0], C) → A'_4
  48. Vector(A, A'_4) → v
  49. Dilate(I, If[7 < o ≤ 8, 8 - o, 0], I') → I'_2
  50. Vector(I, I'_2) → w
  51. Dilate(A, If[5 < o ≤ 6, 6 - o, 0], I') → A'_5
  52. Dilate(A, If[6 < o ≤ 7, 7 - o, 0], I) → A'_6
  53. Vector(A, A'_6) → u_1
  54. Translate(A, u_1) → A'_7
  55. Translate(A'_5, u_1) → Q
  56. Segment(I, C) → l_1
  57. Angle(L, A, I') → γ
  58. Rotate(A'_7, If[11 < o ≤ 12, ((-(o - 11)) * (2 * γ)), (-2 * γ)], I) → R
  59. Rotate(Q, If[7 < o ≤ 8, (((-(o - 7)) * 2) * γ), (-2 * γ)], I) → Q'
  60. Polygon(A, C, I', I) → poly1, a_2, c_2, i', i_2
  61. Midpoint(a_1) → S
  62. Midpoint(t) → T
  63. Midpoint(s) → U
  64. Midpoint(r) → V
  65. Dilate(A, If[5.5 < o ≤ 6.5, 6.5 - o, 0], S) → A'_8
  66. Dilate(I, If[5.5 < o ≤ 6.5, 6.5 - o, 0], T) → I'_3
  67. Dilate(I', If[5.5 < o ≤ 6.5, 6.5 - o, 0], U) → I''
  68. Dilate(C, If[5.5 < o ≤ 6.5, 6.5 - o, 0], V) → C'
  69. Segment(A, A'_8) → f_1
  70. Segment(I, I'_3) → h_1
  71. Segment(I', I'') → i_1
  72. Segment(C, C') → j_1
  73. Rotate(A, If[6.5 < o ≤ 7.5, ((-(o - 6.5)) * π), (-π)], S) → A'_9
  74. Rotate(A'_8, If[6.5 < o ≤ 7.5, ((-(o - 6.5)) * π), (-π)], S) → W
  75. Segment(A'_9, W) → k_1
  76. Rotate(I, If[6.5 < o ≤ 7.5, ((-(o - 6.5)) * π), (-π)], T) → I'_4
  77. Rotate(I'_3, If[6.5 < o ≤ 7.5, ((-(o - 6.5)) * π), (-π)], T) → Z
  78. Segment(I'_4, Z) → m_1
  79. Rotate(I', If[6.5 < o ≤ 7.5, ((-(o - 6.5)) * π), (-π)], U) → I''_1
  80. Rotate(I'', If[6.5 < o ≤ 7.5, ((-(o - 6.5)) * π), (-π)], U) → I'''
  81. Segment(I''_1, I''') → n_1
  82. Rotate(C, If[6.5 < o ≤ 7.5, ((-(o - 6.5)) * π), (-π)], V) → C'_1
  83. Rotate(C', If[6.5 < o ≤ 7.5, ((-(o - 6.5)) * π), (-π)], V) → C''
  84. Segment(C'_1, C'') → p_1
  85. Dilate(V, If[7.5 < o ≤ 8.5, 8.5 - o, 0], S) → V'
  86. Segment(V, V') → q_1
  87. Angle(V, S, T) → δ
  88. Rotate(V, If[8.5 < o ≤ 9.5, ((o - 8.5) * δ), δ], S) → V'_1
  89. Rotate(V', If[8.5 < o ≤ 9.5, ((o - 8.5) * δ), δ], S) → V''
  90. Segment(V'_1, V'') → r_1
  91. Rotate(V'_1, If[9.5 < o ≤ 10.5, ((o - 9.5) * (π - δ)), π - δ], T) → A_1
  92. Rotate(V'', If[9.5 < o ≤ 10.5, ((o - 9.5) * (π - δ)), π - δ], T) → V'''
  93. Segment(A_1, V''') → s_1
  94. Rotate(A_1, If[10.5 < o ≤ 11.5, ((o - 10.5) * δ), δ], U) → B_1
  95. Rotate(V''', If[10.5 < o ≤ 11.5, ((o - 10.5) * δ), δ], U) → C_1
  96. Segment(B_1, C_1) → t_1
  97. Polygon(A, V, S) → poly2, s_2, a_3, v_1
  98. Polygon(S, I, T) → poly3, t_2, s_3, i_3
  99. Polygon(T, U, I') → poly4, i'_1, t_3, u_2
  100. Polygon(V, C, U) → poly5, u_3, v_2, c_3
  101. Polygon(V, U, T, S) → poly6, v_3, u_4, t_4, s_4

AI Drawing Prompt Reference

Draw a rhombus and perform a mirror transformation around point C, then a scale transformation around point I, followed by a rotation transformation around point C. Finally, show the dynamic changes of the rhombus under different transformations.
The prompt above was compiled from the original drawing commands and is for reference only.