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Geometric Transformations and Function Graphs by Juan Carlos Ponce Campuzano

Geometric Transformations and Function Graphs by Juan Carlos Ponce Campuzano
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2019-01-10 10:59
FunctionTrigonometryTransformation
In collections GeoGebraScript for Making Constructions and Animations
This example demonstrates geometric transformations, including translation and dilation, and shows how to draw function graphs using GeoGebra. Key mathematical concepts include functions, trigonometry, and transformations. The specific implementation can be understood through commands like Sequence, Polygon, and Dilate in the construction summary. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Sequence(((t * cos(((k * 2) * π / 3) + π / 2)), (t * sin(((k * 2) * π / 3) + π / 2))), k, 0, 2) → Points
  2. Sequence(((((-t) + 1.5) * cos(((k * 2) * π / 3) + (3 * π / 2))), (((-t) + 1.5) * sin(((k * 2) * π / 3) + (3 * π / 2)))), k, 0, 2) → Points1
  3. Polygon(A1, B2, A3, B1, A2, B3) → triangle, a1, b2, a3, b1, a2, b3
  4. Dilate(A1, 1 / 10, (0, 0)) → A1'
  5. Dilate(B2, 1 / 10, (0, 0)) → B2'
  6. Dilate(A3, 1 / 10, (0, 0)) → A3'
  7. Dilate(B1, 1 / 10, (0, 0)) → B1'
  8. Dilate(A2, 1 / 10, (0, 0)) → A2'
  9. Dilate(B3, 1 / 10, (0, 0)) → B3'
  10. Polygon(Dilate[A1, 1 / 10, (0, 0)], Dilate[B2, 1 / 10, (0, 0)], Dilate[A3, 1 / 10, (0, 0)], Dilate[B1, 1 / 10, (0, 0)], Dilate[A2, 1 / 10, (0, 0)], Dilate[B3, 1 / 10, (0, 0)]) → C1, f, g, h, i, j, k
  11. Dilate(A1, 2 / 10, (0, 0)) → A1'_1
  12. Dilate(B2, 2 / 10, (0, 0)) → B2'_1
  13. Dilate(A3, 2 / 10, (0, 0)) → A3'_1
  14. Dilate(B1, 2 / 10, (0, 0)) → B1'_1
  15. Dilate(A2, 2 / 10, (0, 0)) → A2'_1
  16. Dilate(B3, 2 / 10, (0, 0)) → B3'_1
  17. Polygon(Dilate[A1, 2 / 10, (0, 0)], Dilate[B2, 2 / 10, (0, 0)], Dilate[A3, 2 / 10, (0, 0)], Dilate[B1, 2 / 10, (0, 0)], Dilate[A2, 2 / 10, (0, 0)], Dilate[B3, 2 / 10, (0, 0)]) → C2, l, m, n, p, q, r
  18. Dilate(A1, 3 / 10, (0, 0)) → A1'_2
  19. Dilate(B2, 3 / 10, (0, 0)) → B2'_2
  20. Dilate(A3, 3 / 10, (0, 0)) → A3'_2
  21. Dilate(B1, 3 / 10, (0, 0)) → B1'_2
  22. Dilate(A2, 3 / 10, (0, 0)) → A2'_2
  23. Dilate(B3, 3 / 10, (0, 0)) → B3'_2
  24. Polygon(Dilate[A1, 3 / 10, (0, 0)], Dilate[B2, 3 / 10, (0, 0)], Dilate[A3, 3 / 10, (0, 0)], Dilate[B1, 3 / 10, (0, 0)], Dilate[A2, 3 / 10, (0, 0)], Dilate[B3, 3 / 10, (0, 0)]) → C3, s, a, b, c, d, e
  25. Dilate(A1, 4 / 10, (0, 0)) → A1'_3
  26. Dilate(B2, 4 / 10, (0, 0)) → B2'_3
  27. Dilate(A3, 4 / 10, (0, 0)) → A3'_3
  28. Dilate(B1, 4 / 10, (0, 0)) → B1'_3
  29. Dilate(A2, 4 / 10, (0, 0)) → A2'_3
  30. Dilate(B3, 4 / 10, (0, 0)) → B3'_3
  31. Polygon(Dilate[A1, 4 / 10, (0, 0)], Dilate[B2, 4 / 10, (0, 0)], Dilate[A3, 4 / 10, (0, 0)], Dilate[B1, 4 / 10, (0, 0)], Dilate[A2, 4 / 10, (0, 0)], Dilate[B3, 4 / 10, (0, 0)]) → C4, f_1, g_1, h_1, i_1, j_1, k_1
  32. Dilate(A1, 5 / 10, (0, 0)) → A1'_4
  33. Dilate(B2, 5 / 10, (0, 0)) → B2'_4
  34. Dilate(A3, 5 / 10, (0, 0)) → A3'_4
  35. Dilate(B1, 5 / 10, (0, 0)) → B1'_4
  36. Dilate(A2, 5 / 10, (0, 0)) → A2'_4
  37. Dilate(B3, 5 / 10, (0, 0)) → B3'_4
  38. Polygon(Dilate[A1, 5 / 10, (0, 0)], Dilate[B2, 5 / 10, (0, 0)], Dilate[A3, 5 / 10, (0, 0)], Dilate[B1, 5 / 10, (0, 0)], Dilate[A2, 5 / 10, (0, 0)], Dilate[B3, 5 / 10, (0, 0)]) → C5, l_1, m_1, n_1, p_1, q_1, r_1
  39. Dilate(A1, 6 / 10, (0, 0)) → A1'_5
  40. Dilate(B2, 6 / 10, (0, 0)) → B2'_5
  41. Dilate(A3, 6 / 10, (0, 0)) → A3'_5
  42. Dilate(B1, 6 / 10, (0, 0)) → B1'_5
  43. Dilate(A2, 6 / 10, (0, 0)) → A2'_5
  44. Dilate(B3, 6 / 10, (0, 0)) → B3'_5
  45. Polygon(Dilate[A1, 6 / 10, (0, 0)], Dilate[B2, 6 / 10, (0, 0)], Dilate[A3, 6 / 10, (0, 0)], Dilate[B1, 6 / 10, (0, 0)], Dilate[A2, 6 / 10, (0, 0)], Dilate[B3, 6 / 10, (0, 0)]) → C6, s_1, t_1, a_1, b_1, c_1, d_1
  46. Dilate(A1, 7 / 10, (0, 0)) → A1'_6
  47. Dilate(B2, 7 / 10, (0, 0)) → B2'_6
  48. Dilate(A3, 7 / 10, (0, 0)) → A3'_6
  49. Dilate(B1, 7 / 10, (0, 0)) → B1'_6
  50. Dilate(A2, 7 / 10, (0, 0)) → A2'_6
  51. Dilate(B3, 7 / 10, (0, 0)) → B3'_6
  52. Polygon(Dilate[A1, 7 / 10, (0, 0)], Dilate[B2, 7 / 10, (0, 0)], Dilate[A3, 7 / 10, (0, 0)], Dilate[B1, 7 / 10, (0, 0)], Dilate[A2, 7 / 10, (0, 0)], Dilate[B3, 7 / 10, (0, 0)]) → C7, e_1, f_2, g_2, h_2, i_2, j_2
  53. Dilate(A1, 8 / 10, (0, 0)) → A1'_7
  54. Dilate(B2, 8 / 10, (0, 0)) → B2'_7
  55. Dilate(A3, 8 / 10, (0, 0)) → A3'_7
  56. Dilate(B1, 8 / 10, (0, 0)) → B1'_7
  57. Dilate(A2, 8 / 10, (0, 0)) → A2'_7
  58. Dilate(B3, 8 / 10, (0, 0)) → B3'_7
  59. Polygon(Dilate[A1, 8 / 10, (0, 0)], Dilate[B2, 8 / 10, (0, 0)], Dilate[A3, 8 / 10, (0, 0)], Dilate[B1, 8 / 10, (0, 0)], Dilate[A2, 8 / 10, (0, 0)], Dilate[B3, 8 / 10, (0, 0)]) → C8, k_2, l_2, m_2, n_2, p_2, q_2
  60. Dilate(A1, 9 / 10, (0, 0)) → A1'_8
  61. Dilate(B2, 9 / 10, (0, 0)) → B2'_8
  62. Dilate(A3, 9 / 10, (0, 0)) → A3'_8
  63. Dilate(B1, 9 / 10, (0, 0)) → B1'_8
  64. Dilate(A2, 9 / 10, (0, 0)) → A2'_8
  65. Dilate(B3, 9 / 10, (0, 0)) → B3'_8
  66. Polygon(Dilate[A1, 9 / 10, (0, 0)], Dilate[B2, 9 / 10, (0, 0)], Dilate[A3, 9 / 10, (0, 0)], Dilate[B1, 9 / 10, (0, 0)], Dilate[A2, 9 / 10, (0, 0)], Dilate[B3, 9 / 10, (0, 0)]) → C9, r_2, s_2, t_2, a_2, b_2, c_2
  67. Dilate(A1, 10 / 10, (0, 0)) → A1'_9
  68. Dilate(B2, 10 / 10, (0, 0)) → B2'_9
  69. Dilate(A3, 10 / 10, (0, 0)) → A3'_9
  70. Dilate(B1, 10 / 10, (0, 0)) → B1'_9
  71. Dilate(A2, 10 / 10, (0, 0)) → A2'_9
  72. Dilate(B3, 10 / 10, (0, 0)) → B3'_9
  73. Polygon(Dilate[A1, 10 / 10, (0, 0)], Dilate[B2, 10 / 10, (0, 0)], Dilate[A3, 10 / 10, (0, 0)], Dilate[B1, 10 / 10, (0, 0)], Dilate[A2, 10 / 10, (0, 0)], Dilate[B3, 10 / 10, (0, 0)]) → C10, d_2, e_2, f_3, g_3, h_3, i_3