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2D Vectors and Reflection Geometric Construction by Claudio Martínez Gil

2D Vectors and Reflection Geometric Construction by Claudio Martínez Gil
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2020-05-26 23:26
VectorFunctionGeometric Construction
This example demonstrates the interaction between 2D vectors, reflection, function graphs, and geometric shapes. Core math concepts include vector operations, function graphing, reflection transformations, and analytical geometry. Construction highlights involve using GeoGebra commands like Line, Vector, OrthogonalVector, LineBisector, OrthogonalLine, Mirror, Intersect, Polygon, CircleArc. Suitable for high school mathematics education to understand the geometric significance of vectors, reflection, function graphs, and optimization problems.

GeoGebra Commands & Parameters

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

AI Drawing Prompt Reference

Draw a geometric construction of 2D vectors and reflection, including two vectors and their reflection lines, showing the interaction of vector operations, function graphs, and geometric shapes. Start by drawing a line segment and two vectors, then find the orthogonal vector of one, and draw two perpendicular lines. Next, use bisectors and reflection transformations to construct multiple points and geometric shapes like polygons and circular arcs, finally presenting a complex geometric figure that illustrates the integration of vectors, reflection, function graphs, and analytical geometry.
The prompt above was compiled from the original drawing commands and is for reference only.