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Symmetry with respect to axes

Symmetry with respect to axes
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2021-05-06 15:26
Coordinate GeometryTransformationGeometric Construction
In collections Mat 1 ESO - IESO LA PAZ
This example demonstrates geometric constructions using symmetry axes. Key mathematical concepts include symmetry, axial symmetry, and geometric construction. Construction involves GeoGebra commands like Line, Intersect, and Vector, and objects such as p1texto3, p1texto4. Suitable for middle or high school mathematics teaching to understand symmetric figures and coordinate geometry.

GeoGebra Commands & Parameters

  1. Line(A_0, a) → b
  2. Textfield(p2c1) → p2CasillaDeEntrada1
  3. Textfield(p2c2) → p2CasillaDeEntrada2
  4. Random(-7, 7) → n1
  5. Random(-7, 7) → n2
  6. Polygon(C, D, G, F) → polígono1, c, d, g, f
  7. Polygon(C, H, I, F) → polígono2, c_1, h, i, f_1
  8. Segment(Y_8, Y_{-8}) → j
  9. Vector(Y_{-8}, Y_8) → ejeY
  10. Vector(Centro, A_8) → ejeX
  11. Line(A_1, ejeY) → e
  12. Line(A_2, ejeY) → k
  13. Line(A_3, ejeY) → l
  14. Line(A_4, ejeY) → m
  15. Line(A_5, ejeY) → n
  16. Line(A_6, ejeY) → p
  17. Line(A_7, ejeY) → q
  18. Line(Y_1, ejeX) → r
  19. Line(Y_2, ejeX) → s
  20. Line(Y_3, ejeX) → a_1
  21. Line(Y_4, ejeX) → b_1
  22. Line(Y_5, ejeX) → d_1
  23. Line(Y_6, ejeX) → e_1
  24. Line(Y_7, ejeX) → g_1
  25. Line(A_{-1}, ejeY) → h_1
  26. Line(A_{-2}, ejeY) → i_1
  27. Line(A_{-3}, ejeY) → j_1
  28. Line(A_{-4}, ejeY) → k_1
  29. Line(A_{-5}, ejeY) → l_1
  30. Line(A_{-6}, ejeY) → m_1
  31. Line(A_{-7}, ejeY) → n_1
  32. Line(Y_{-1}, ejeX) → p_1
  33. Line(Y_{-2}, ejeX) → q_1
  34. Line(Y_{-3}, ejeX) → r_1
  35. Line(Y_{-4}, ejeX) → s_1
  36. Line(Y_{-5}, ejeX) → t_1
  37. Line(Y_{-6}, ejeX) → a_2
  38. Line(Y_{-7}, ejeX) → b_2
  39. Line(Centro, ejeY) → c_2
  40. Line(Y_8, ejeX) → d_2
  41. Line(Y_{-8}, ejeX) → e_2
  42. Line(A_8, ejeY) → f_2
  43. Intersect(r, c_2) → A
  44. Intersect(s, c_2) → B
  45. Intersect(a_1, c_2) → E
  46. Intersect(b_1, c_2) → J
  47. Intersect(d_1, c_2) → K
  48. Intersect(e_1, c_2) → L
  49. Intersect(g_1, c_2) → M
  50. Intersect(d_2, g_1) → G_1
  51. Intersect(p_1, c_2) → H_1
  52. Intersect(q_1, c_2) → I_1
  53. Intersect(r_1, c_2) → J_1
  54. Intersect(s_1, c_2) → K_1
  55. Intersect(t_1, c_2) → L_1
  56. Intersect(a_2, c_2) → M_1
  57. Intersect(b_2, c_2) → N_1
  58. Ray(M, Y_7) → g_2
  59. Ray(L, Y_6) → h_2
  60. Ray(K, Y_5) → i_2
  61. Ray(J, Y_4) → j_2
  62. Ray(E, Y_3) → k_2
  63. Ray(B, Y_2) → l_2
  64. Ray(A, Y_1) → m_2
  65. Ray(H_1, Y_{-1}) → n_2
  66. Ray(I_1, Y_{-2}) → p_2
  67. Ray(J_1, Y_{-3}) → q_2
  68. Ray(K_1, Y_{-4}) → r_2
  69. Ray(L_1, Y_{-5}) → s_2
  70. Ray(M_1, Y_{-6}) → t_2
  71. Ray(N_1, Y_{-7}) → a_3
  72. Intersect(m, k_2) → N
  73. Vector(A_0, A_4) → w
  74. Vector(A_0, Y_3) → u_1
  75. Vector(A_4, N) → v_1
  76. Vector(Y_3, N) → w_1
  77. Vector(A_0, (x(A_0), y(A_0) + ((n2 * (x(Corner[2]) - x(A_0)))) / 8)) → w_2
  78. Vector(A_0, Y_3) → v_3
  79. Vector(Y_3, O) → w_3
  80. Vector(Y_3, P) → b_3
  81. Vector((x(A_0), y(A_0)), (x(A_0), y(A_0) + ((n2 * (x(Corner[2]) - x(A_0)))) / 8)) → v_2
  82. Vector((x(A_0), y(A_0) + ((n2 * (x(Corner[2]) - x(A_0)))) / 8), (x(A_0) + ((n1 * (x(Corner[2]) - x(A_0)))) / 8, y(A_0) + ((n2 * (x(Corner[2]) - x(A_0)))) / 8)) → u_2
  83. Vector((x(A_0), y(A_0) + ((n2 * (x(Corner[2]) - x(A_0)))) / 8), (x(A_0) + (((-n1) * (x(Corner[2]) - x(A_0)))) / 8, y(A_0) + ((n2 * (x(Corner[2]) - x(A_0)))) / 8)) → u_3
  84. Vector((x(A_0) + (n1 * (x(Corner[2]) - x(A_0)) / 8), y(A_0)), (x(A_0) + ((n1 * (x(Corner[2]) - x(A_0)))) / 8, y(A_0) + ((n2 * (x(Corner[2]) - x(A_0)))) / 8)) → vectorx
  85. Vector((x(A_0) + (n1 * (x(Corner[2]) - x(A_0)) / 8), y(A_0)), (x(A_0) + ((n1 * (x(Corner[2]) - x(A_0)))) / 8, y(A_0) + (((-n2) * (x(Corner[2]) - x(A_0)))) / 8)) → vectorsimétricox

AI Drawing Prompt Reference

Draw a coordinate system with two perpendicular axes named X-axis and Y-axis. Randomly select two points A and B on the X-axis, and choose point C as the symmetry center on the Y-axis. Construct two quadrilaterals polígono1 and polígono2 with C as a vertex, and the other vertices being D, G, F and H, I, F respectively. Then, construct two horizontal lines r and s, and two vertical lines a_1 and b_1 through point C and the Y-axis to determine the vertices of the quadrilaterals.
The prompt above was compiled from the original drawing commands and is for reference only.