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2D Vectors and Reflection Geometric Construction

2D Vectors and Reflection Geometric Construction
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2020-05-29 23:05
VectorOptimizationGeometric Construction
This example demonstrates the geometric relationships and constructions involving 2D vectors, reflection, squares, and equilateral triangles. It covers core mathematical concepts such as vector operations, reflection transformations, properties of squares and equilateral triangles, slope calculations, and difference computations. The construction uses GeoGebra commands and objects like Line, OrthogonalLine, Vector, OrthogonalVector, LineBisector, Mirror, Intersect, Polygon, CircleArc, and Segment. Suitable for high school mathematics teaching to understand vectors, reflections, geometric transformations, and optimization problems.

GeoGebra Commands & Parameters

  1. Line(A, B) → s
  2. OrthogonalLine(A, s) → b
  3. Vector(A, B) → u
  4. OrthogonalVector(u) → v
  5. OrthogonalLine(F, b) → f
  6. LineBisector(A_1, A) → l
  7. Mirror(f, l) → f'
  8. OrthogonalLine(D, s) → i
  9. Intersect(i, f') → E
  10. LineBisector(A, B) → m
  11. Intersect(i, l) → P
  12. OrthogonalLine(B, u, xOyPlane) → g
  13. Mirror(i, m) → i'
  14. OrthogonalLine(A_1, b) → r
  15. Intersect(g, r) → C
  16. Intersect(m, l) → L
  17. Mirror(f, l) → f'_1
  18. Intersect(m, f) → M
  19. Mirror(F, l) → F'
  20. Intersect(m, f') → S
  21. Polygon(A_1, C, B, A) → c4, a_1, c_3, b_2, a_2
  22. OrthogonalLine(K, r) → h
  23. OrthogonalLine(H, m) → k
  24. Intersect(i', f') → W
  25. Mirror(k, l) → k'
  26. OrthogonalLine(O, f'_1) → j
  27. OrthogonalLine(Q, f'_1) → n
  28. Intersect(k', j) → Z
  29. Intersect(k', i) → G_1
  30. OrthogonalLine(E_1, r) → p
  31. OrthogonalLine(G, b) → q
  32. Intersect(m, f'_1) → H_1
  33. Intersect(q, m) → I_1
  34. Intersect(k', p) → J_1
  35. Intersect(q, p) → K_1
  36. Polygon(H_1, I_1, K_1, J_1, G_1, E) → polígono1, h_1, i_1, k_1, j_1, g_1, e
  37. Mirror(K_1, m) → N_1
  38. Mirror(J_1, m) → O_1
  39. Mirror(G_1, m) → P_1
  40. Mirror(E, m) → E'
  41. Polygon(L_1, M_1, N_1, O_1, P_1, E') → polígono1', l_1, m_1, n_1, o_1, p_1, e'
  42. Line(Z, F_1) → t
  43. Intersect(k, t) → Q_1
  44. Intersect(j, k) → R_1
  45. Intersect(n, k) → S_1
  46. OrthogonalLine(V, g, xOyPlane) → a
  47. OrthogonalLine(B_1, g, xOyPlane) → c
  48. OrthogonalLine(C_1, g, xOyPlane) → d
  49. OrthogonalLine(D_1, g, xOyPlane) → f_1
  50. OrthogonalLine(F_1, g, xOyPlane) → q_1
  51. Intersect(h, a) → N
  52. Intersect(h, c) → T_1
  53. Intersect(j, c) → U_1
  54. Intersect(t, n) → V_1
  55. Polygon(S_1, R_1, N, T_1, U_1, Z, V_1) → polígono2, s_1, r_1, n_2, t_1, u_1, z_1, v_1
  56. LineBisector(N, R_1, xOyPlane) → b_1
  57. Intersect(b_1, k) → W_1
  58. CircleArc(W_1, N, R_1, xOyPlane) → c_1
  59. Line(D_1, t) → d_1
  60. Intersect(d_1, k) → Z_1
  61. Polygon(D_1, F_1, Q_1, Z_1) → c1, f_2, g_2, h_2, i_2
  62. Intersect(t, f_1) → A_2
  63. Intersect(t, d) → B_2
  64. OrthogonalLine(T, r) → k_2
  65. Intersect(k_2, k') → D_2
  66. Line(A_2, D_2) → l_2
  67. Line(B_2, l_2) → j_2
  68. Intersect(j_2, k') → J
  69. Polygon(A_2, D_2, J, B_2) → c2, m_2, d_2, j_3, p_2
  70. LineBisector(G_1, M) → q_2
  71. Intersect(q_2, m) → C_2
  72. CircleArc(C_2, G_1, M) → c_2
  73. CircleArc(C_2, J_1, E_2) → r_2
  74. Polygon(G_1, J_1, E_2, M) → c3, s_2, t_2, f_3, m_3
  75. Mirror(c_2, m) → d_3
  76. Mirror(r_2, m) → e_3
  77. Mirror(G_1, m) → F_2
  78. Mirror(J_1, m) → G_2
  79. Mirror(E_2, m) → H_2
  80. Mirror(M, m) → M'
  81. Polygon(F_2, G_2, H_2, M') → c3', g_3, h_3, i_3, m'
  82. Segment(J_1, E_2) → k_3
  83. Segment(E_2, O_1) → l_3
  84. Segment(R_1, N) → n_3