MathPlotAI Logo MathPlotAI

Homothety & Symmetry

Homothety & Symmetry
Loading the math board and drawing, please wait…
2018-07-22 06:35
PolygonTransformationGeometric Construction
In collections Homothety, Rotation Symmetry -RO
This example demonstrates the application of homothety (scaling) and symmetry (reflection) in geometric figures. Core math concepts include the properties of homothety, the determination of symmetry axes, and polygon construction. Construction highlights involve using commands/objects like Segment, OrthogonalLine, Point, Intersect, Polygon, AngularBisector, Dilate, and Mirror. Suitable for high school students learning geometric transformations and symmetry.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. OrthogonalLine(A, f) → g
  3. OrthogonalLine(B, f) → h
  4. Point(g) → C
  5. OrthogonalLine(C, g) → i
  6. Intersect(h, i) → D
  7. Polygon(C, D, B, A) → q1, c, d, b, a
  8. Polygon(C, B, D) → t1, d_1, c_1, b_1
  9. AngularBisector(D, C, B) → j
  10. Segment(D, A) → k
  11. Intersect(k, d_1) → E
  12. Point(k) → F
  13. Dilate(C, 9 / 10, F) → C'
  14. Dilate(B, 9 / 10, F) → B'
  15. Dilate(D, 9 / 10, F) → D'
  16. Polygon(C', B', D') → t1', d', c', b'
  17. Dilate(C, 8 / 10, F) → C'_1
  18. Dilate(B, 8 / 10, F) → B'_1
  19. Dilate(D, 8 / 10, F) → D'_1
  20. Polygon(C'_1, B'_1, D'_1) → t1'_1, d'_1, c'_1, b'_1
  21. Dilate(C, 7 / 10, F) → C'_2
  22. Dilate(B, 7 / 10, F) → B'_2
  23. Dilate(D, 7 / 10, F) → D'_2
  24. Polygon(C'_2, B'_2, D'_2) → t1'_2, d'_2, c'_2, b'_2
  25. Dilate(C, 6 / 10, F) → C'_3
  26. Dilate(B, 6 / 10, F) → B'_3
  27. Dilate(D, 6 / 10, F) → D'_3
  28. Polygon(C'_3, B'_3, D'_3) → t1'_3, d'_3, c'_3, b'_3
  29. Dilate(C, 5 / 10, F) → C'_4
  30. Dilate(B, 5 / 10, F) → B'_4
  31. Dilate(D, 5 / 10, F) → D'_4
  32. Polygon(C'_4, B'_4, D'_4) → t1'_4, d'_4, c'_4, b'_4
  33. Dilate(C, 4 / 10, F) → C'_5
  34. Dilate(B, 4 / 10, F) → B'_5
  35. Dilate(D, 4 / 10, F) → D'_5
  36. Polygon(C'_5, B'_5, D'_5) → t1'_5, d'_5, c'_5, b'_5
  37. Dilate(C, 3 / 10, F) → C'_6
  38. Dilate(B, 3 / 10, F) → B'_6
  39. Dilate(D, 3 / 10, F) → D'_6
  40. Polygon(C'_6, B'_6, D'_6) → t1'_6, d'_6, c'_6, b'_6
  41. Dilate(C, 2 / 10, F) → C'_7
  42. Dilate(B, 2 / 10, F) → B'_7
  43. Dilate(D, 2 / 10, F) → D'_7
  44. Polygon(C'_7, B'_7, D'_7) → t1'_7, d'_7, c'_7, b'_7
  45. Mirror(C', E) → C''
  46. Mirror(B', E) → B''
  47. Mirror(D', E) → D''
  48. Polygon(C'', B'', D'') → t1'', d'', c'', b''
  49. Mirror(C', E) → C''_1
  50. Mirror(B', E) → B''_1
  51. Mirror(D', E) → D''_1
  52. Mirror(C'_1, E) → G
  53. Mirror(B'_1, E) → H
  54. Mirror(D'_1, E) → I
  55. Polygon(G, H, I) → t2, i_1, g_1, h_1
  56. Mirror(C'_2, E) → J
  57. Mirror(B'_2, E) → K
  58. Mirror(D'_2, E) → L
  59. Polygon(J, K, L) → t3, l, j_1, k_1
  60. Mirror(C'_3, E) → M
  61. Mirror(B'_3, E) → N
  62. Mirror(D'_3, E) → O
  63. Polygon(M, N, O) → t4, o, m, n
  64. Mirror(C'_4, E) → P
  65. Mirror(B'_4, E) → Q
  66. Mirror(D'_4, E) → R
  67. Polygon(P, Q, R) → t5, r, p, q
  68. Mirror(C'_5, E) → S
  69. Mirror(B'_5, E) → T
  70. Mirror(D'_5, E) → U
  71. Polygon(S, T, U) → t6, u, s, t
  72. Mirror(C'_6, E) → V
  73. Mirror(B'_6, E) → W
  74. Mirror(D'_6, E) → Z
  75. Polygon(V, W, Z) → t7, z_1, v, w
  76. Mirror(C'_7, E) → A_1
  77. Mirror(B'_7, E) → B_1
  78. Mirror(D'_7, E) → C_1
  79. Polygon(A_1, B_1, C_1) → t8, c_2, a_1, b_2