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Symmetry and Translation by leucotea

Symmetry and Translation by leucotea
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2012-11-18 00:00
DerivativeTransformationGeometric Construction
This example demonstrates the construction of symmetric figures. Key mathematical concepts include symmetry and translation. Using GeoGebra commands such as Line, Polygon, Intersect, Segment, Mirror, etc., symmetric figures can be constructed. Suitable for students at the junior high school level and above for learning geometric transformations.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Line(C, D) → b
  3. Polygon(E, F, G, H) → poli1, e, f, g, h
  4. Intersect(e, a) → I
  5. Intersect(a, g) → J
  6. Intersect(b, g) → K
  7. Intersect(b, e) → L
  8. Segment(I, J) → c
  9. Segment(L, K) → d
  10. Polygon(C_1, Q, B_1, M, N, O, P, R, S, T, U, V, W, Z, A_1) → poli2, c_1, a_1, b_1, m, n, o, p, q, r, s, t, u, v, w, z
  11. Polygon(E_1, F_1, O_1, P_1, Q_1, R_1, S_1, G_1, H_1, I_1, J_1, K_1, L_1, M_1, N_1) → poli3, e_1, n_1, o_1, p_1, q_1, r_1, s_1, f_1, g_1, h_1, i_1, j_1, k_1, l_1, m_1
  12. Polygon(T_1, U_1, F_2, G_2, H_2, I_2, J_2, V_1, W_1, Z_1, A_2, B_2, C_2, D_2, E_2) → poli4, t_1, e_2, f_2, g_2, h_2, i_2, j_2, u_1, v_1, w_1, z_1, a_2, b_2, c_2, d_2
  13. Mirror(C_1, c) → K_2
  14. Mirror(Q, c) → Q'
  15. Mirror(R, c) → R'
  16. Mirror(S, c) → S'
  17. Mirror(T, c) → T'
  18. Mirror(U, c) → U'
  19. Mirror(V, c) → V'
  20. Mirror(W, c) → W'
  21. Mirror(Z, c) → Z'
  22. Mirror(A_1, c) → L_2
  23. Mirror(B_1, c) → M_2
  24. Mirror(M, c) → M'
  25. Mirror(N, c) → N'
  26. Mirror(O, c) → O'
  27. Mirror(P, c) → P'
  28. Polygon(K_2, Q', M_2, M', N', O', P', R', S', T', U', V', W', Z', L_2) → poli2', k_2, l_2, m_2, m', n', o', p', q', r', s', t', u', v', w', z'
  29. Mirror(K_2, d) → N_2
  30. Mirror(Q', d) → Q''
  31. Mirror(R', d) → R''
  32. Mirror(S', d) → S''
  33. Mirror(T', d) → T''
  34. Mirror(U', d) → U''
  35. Mirror(V', d) → V''
  36. Mirror(W', d) → W''
  37. Mirror(Z', d) → Z''
  38. Mirror(L_2, d) → O_2
  39. Mirror(M_2, d) → P_2
  40. Mirror(M', d) → M''
  41. Mirror(N', d) → N''
  42. Mirror(O', d) → O''
  43. Mirror(P', d) → P''
  44. Polygon(N_2, Q'', P_2, M'', N'', O'', P'', R'', S'', T'', U'', V'', W'', Z'', O_2) → poli2'', n_2, o_2, p_2, m'', n'', o'', p'', q'', r'', s'', t'', u'', v'', w'', z''
  45. Mirror(D_1, c) → Q_2
  46. Mirror(Q_2, d) → R_2
  47. If(S_2 ≟ Q_2, 1, 0) → a1
  48. If(T_2 ≟ R_2, 1, 0) → b1
  49. If(L_1 ≟ S' ∧ K_1 ≟ R', 2, 0) → a2
  50. If(D_2 ≟ S'' ∧ E_2 ≟ R'', 2, 0) → b2
  51. If(J_1 ≟ Q' ∧ I_1 ≟ K_2, 2, 0) → a3
  52. If(F_2 ≟ Q'' ∧ G_2 ≟ N_2, 2, 0) → b3
  53. If(H_2 ≟ P'' ∧ I_2 ≟ O'', 2, 0) → b4
  54. If(H_1 ≟ P' ∧ G_1 ≟ O', 2, 0) → a4
  55. If(F_1 ≟ N', 1, 0) → a5
  56. If(J_2 ≟ N'', 1, 0) → b5
  57. If(E_1 ≟ M', 1, 0) → a6
  58. If(T_1 ≟ M'', 1, 0) → b6
  59. If(S_1 ≟ M_2, 1, 0) → a7
  60. If(U_1 ≟ P_2, 1, 0) → b7
  61. If(R_1 ≟ L_2, 1, 0) → a8
  62. If(V_1 ≟ O_2, 1, 0) → b8
  63. If(Q_1 ≟ Z', 1, 0) → a9
  64. If(W_1 ≟ Z'', 1, 0) → b9
  65. If(P_1 ≟ W', 1, 0) → a10
  66. If(Z_1 ≟ W'', 1, 0) → b10
  67. If(O_1 ≟ V', 1, 0) → a11
  68. If(A_2 ≟ V'', 1, 0) → b11
  69. If(N_1 ≟ U', 1, 0) → a12
  70. If(B_2 ≟ U'', 1, 0) → b12
  71. If(M_1 ≟ T', 1, 0) → a13
  72. If(C_2 ≟ T'', 1, 0) → b13
  73. Point(q_2) → U_2

AI Drawing Prompt Reference

Draw a symmetric figure composed of quadrilaterals ABCD and EFGH. First, draw lines AB and CD, then draw quadrilateral EFGH. Find the intersection points I, J, K, and L where lines AB and CD intersect with quadrilateral EFGH, and connect segments IJ and KL. Next, draw a complex polygon C1Q1B1MNPQRUVWZA1 and use mirror operations to generate its symmetric figure C1Q1B1MNPQRUVWZA1'. Finally, use multiple mirror operations to generate the symmetric figure C1Q1B1MNPQRUVWZA1''.
The prompt above was compiled from the original drawing commands and is for reference only.