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二维向量与反射的几何作图

二维向量与反射的几何作图
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2020-05-29 23:05
向量最值优化几何作图
①本范例演示了二维向量、反射、正方形、等边三角形等图形的几何关系与构造；②涉及核心数学概念包括向量运算、反射变换、正方形与等边三角形的性质、斜率与差值计算；③作图要点：运用了Line（直线）、OrthogonalLine（垂线）、Vector（向量）、OrthogonalVector（正交向量）、LineBisector（角平分线）、Mirror（镜像）、Intersect（交点）、Polygon（多边形）、CircleArc（圆弧）、Segment（线段）等GeoGebra命令与对象；④适合高中数学教学，用于理解向量、反射、几何变换及优化问题。

GeoGebra 命令及参数

  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