MathPlotAI Logo MathPlotAI

Kite Diagonals Animation

Kite Diagonals Animation
Loading the math board and drawing, please wait…
2017-02-18 08:37
VectorTransformationGeometric Construction
This example demonstrates the diagonals of a kite and their properties through animation. Key math concepts include perpendicular bisectors, angle bisectors, reflections, and vectors. Construction involves commands like Segment, Midpoint, OrthogonalLine, Point, and transformations such as Dilate and Rotate. Suitable for high school geometry instruction to visualize kite properties and transformations.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Midpoint(a) → C
  3. OrthogonalLine(C, a) → b
  4. Point(b) → E
  5. Point(b) → G_1
  6. Ray(E, G_1) → h_2
  7. Point(h_2) → D
  8. Segment(C, D) → i
  9. Circle(D, (0.3 * i)) → q
  10. Intersect(q, h_2, 1) → H_1
  11. Segment(A, D) → c
  12. Intersect(q, c, 1) → K
  13. Segment(D, B) → d
  14. Segment(B, E) → e
  15. Segment(E, A) → f
  16. Segment(A, C) → g
  17. Circle(A, (0.3 * g)) → h
  18. Circle(B, (0.3 * g)) → k
  19. Segment(C, E) → j
  20. Circle(E, (0.3 * j)) → p
  21. Circle(C, (0.3 * g)) → r
  22. Intersect(h, f, 1) → F
  23. Intersect(h, c, 1) → G
  24. Intersect(k, e, 1) → H
  25. Intersect(k, d, 1) → I
  26. Intersect(q, d, 1) → J
  27. Intersect(p, e, 1) → L
  28. Intersect(b, j) → M
  29. Intersect(b, j) → N
  30. Intersect(b, j) → O
  31. Intersect(b, j) → P
  32. Intersect(b, j) → Q
  33. Intersect(p, b, 2) → R
  34. Intersect(b, i) → S
  35. Intersect(q, b, 1) → T
  36. Intersect(p, f, 1) → U
  37. CircleSector(B, I, H) → s
  38. Angle(A, D, B) → α
  39. Angle(U, E, L) → β
  40. CircleSector(B, H, I) → t
  41. Dilate(D, If[0 < l ≤ 1, 1 - l, 0], A) → D'
  42. Segment(D, D') → m
  43. Rotate(D, If[1 < l ≤ 2, ((l - 1) * α), α], D) → D'_1
  44. Rotate(D', If[1 < l ≤ 2, ((l - 1) * α), α], D) → D''
  45. Segment(D'_1, D'') → m'
  46. Dilate(A, If[2 < l ≤ 3, 3 - l, 0], E) → A'
  47. Segment(A, A') → n
  48. Rotate(A, If[3 < l ≤ 4, ((-(l - 3)) * ((2 * π) - β)), (-((2 * π) - β))], E) → A'_1
  49. Rotate(A', If[3 < l ≤ 4, ((-(l - 3)) * ((2 * π) - β)), (-((2 * π) - β))], E) → A''
  50. Segment(A'_1, A'') → n'
  51. Polygon(E, B, D, A) → poly1, e_1, b_1, d_1, a_1
  52. CircleSector(E, L, R) → f_1
  53. Dilate(D, If[4 < l ≤ 5, 5 - l, 0], E) → D'_2
  54. Segment(D, D'_2) → g_1
  55. Dilate(B, If[5 < l ≤ 6, 6 - l, 0], A) → B'
  56. Vector(B, B') → u
  57. Translate(s, u) → s'
  58. Line(A, e) → h_1
  59. Intersect(h, h_1, 2) → V
  60. Intersect(h, g, 1) → W
  61. Angle(V, A, G) → γ
  62. Rotate(s', If[6 < l ≤ 7, ((l - 6) * γ), γ], A) → s''
  63. CircleSector(D, K, H_1) → c_1
  64. Rotate(f_1, If[8 < l ≤ 9, ((l - 8) * ((2 * π) - β) / 2), ((2 * π) - β) / 2], E) → p_1
  65. Dilate(A, If[9 < l ≤ 10, 10 - l, 0], C) → A'_2
  66. Segment(A, A'_2) → i_1
  67. Dilate(C, If[10 < l ≤ 11, 11 - l, 0], B) → D'_3
  68. Segment(C, D'_3) → j_1
  69. Segment(B, C) → l_1
  70. Intersect(k, l_1, 1) → Z
  71. CircleSector(B, I, Z) → q_1
  72. CircleSector(A, F, W) → r_1
  73. Rotate(C, If[11.5 < l ≤ 12.5, ((l - 11.5) * π), 3.141592653589793], C) → C'
  74. Rotate(D'_3, If[11.5 < l ≤ 12.5, ((l - 11.5) * π), 3.141592653589793], C) → A_1
  75. Segment(C', A_1) → m_1
  76. Dilate(A, If[12.5 < l ≤ 13.5, 13.5 - l, 0], B) → A'_3
  77. Vector(A, A'_3) → v
  78. Translate(r_1, v) → s_1
  79. Line(B, n) → n_1
  80. Point(n_1) → B_1
  81. Ray(B, B_1) → t_1
  82. Point(t_1) → C_1
  83. Angle(H, B, C_1) → δ
  84. Angle(Z, B, H) → ε
  85. Rotate(s_1, If[13.5 < l ≤ 14.5, ((-(l - 13.5)) * (ε + δ)), (-(ε + δ))], B) → c_2
  86. Dilate(B, If[14.5 < l ≤ 15.5, 15.5 - l, 0], A) → B'_1
  87. Vector(B, B'_1) → w
  88. Translate(q_1, w) → d_2
  89. Translate(I, w) → I'
  90. Angle(G, A, I') → ζ
  91. Angle(D, B, C) → η
  92. Rotate(d_2, If[15.5 < l ≤ 16.5, ((-(l - 15.5)) * (ζ + η)), (-(ζ + η))], A) → e_2
  93. Midpoint(A, B) → D_1
  94. Segment(D, E) → a_2
  95. Segment(A, B) → b_2
  96. Intersect(r, a_2, 2) → E_1
  97. Intersect(r, b_2, 2) → F_1
  98. CircleSector(C, E_1, F_1) → f_2
  99. Rotate(f_2, If[16.5 < l ≤ 17.5, ((-(l - 16.5)) * π / 2), -1.5707963267948966], D_1) → g_2
  100. Rotate(c_1, If[7 < l ≤ 8, ((l - 7) * α / 2), α / 2], D) → k_1