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双曲线上下对称变换

双曲线上下对称变换
几何画板及绘图内容加载中，请稍等……
2016-02-15 08:26
向量函数解析几何变换几何作图
所属专题 Conic Section Collection
本范例演示双曲线的上下对称变换。核心数学概念包括双曲线、反射、向量和几何作图。通过使用GeoGebra命令如Line, Segment, Intersect, Tangent, OrthogonalLine, Mirror等，可以直观地展示双曲线的对称性质。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Line(C, A) → a
  2. Segment(C, A) → b
  3. Intersect(c, b) → D, E
  4. Tangent(D, c) → d,
  5. OrthogonalLine(D, d) → e
  6. Line(C, A) → g
  7. Mirror(g, e) → g'
  8. Intersect(c, g') → G, H
  9. Tangent(G, c) → h,
  10. OrthogonalLine(G, h) → i
  11. Mirror(g', i) → g''
  12. Segment(C, D) → j
  13. Segment(D, G) → k
  14. Segment(D, B) → l
  15. Intersect(c, g'') → I, J
  16. Segment(J, G) → m
  17. Segment(G, A) → n
  18. Tangent(J, c) → p,
  19. OrthogonalLine(J, p) → q
  20. Mirror(g'', q) → g'''
  21. Intersect(c, g''') → K, L
  22. Segment(A, B) → r
  23. Segment(J, K) → s
  24. Segment(K, B) → t
  25. Segment(I, B) → a_1
  26. Segment(J, A) → b_1
  27. Tangent(K, c) → c_1,
  28. OrthogonalLine(K, c_1) → d_1
  29. Mirror(g''', d_1) → e_1
  30. Intersect(c, e_1) → M, N
  31. Segment(K, N) → f_1
  32. Segment(K, M) → g_1
  33. Segment(N, A) → h_1
  34. Tangent(N, c) → i_1,
  35. OrthogonalLine(N, i_1) → j_1
  36. Mirror(e_1, j_1) → k_1
  37. Intersect(c, k_1) → O, P
  38. Segment(P, O) → l_1
  39. Segment(O, B) → m_1
  40. Tangent(O, c) → n_1,
  41. OrthogonalLine(O, n_1) → p_1
  42. Mirror(k_1, p_1) → q_1
  43. Intersect(c, q_1) → Q, R
  44. Segment(O, R) → r_1
  45. Segment(R, A) → s_1
  46. Tangent(R, c) → t_1,
  47. OrthogonalLine(R, t_1) → a_2
  48. Mirror(q_1, t_1) → b_2
  49. Intersect(c, b_2) → S, T
  50. Segment(R, T) → c_2
  51. Segment(T, B) → d_2
  52. Tangent(T, c) → e_2,
  53. OrthogonalLine(T, e_2) → f_2
  54. Mirror(b_2, f_2) → g_2
  55. Intersect(c, g_2) → U, V
  56. Segment(T, U) → h_2
  57. Segment(U, A) → i_2
  58. Tangent(U, c) → j_2,
  59. OrthogonalLine(U, j_2) → k_2
  60. Mirror(g_2, k_2) → l_2
  61. Intersect(c, l_2) → W, Z
  62. Segment(U, Z) → m_2
  63. Segment(Z, B) → n_2
  64. Tangent(Z, c) → p_2,
  65. OrthogonalLine(Z, p_2) → q_2
  66. Mirror(l_2, q_2) → r_2
  67. Intersect(c, r_2) → A_1, B_1
  68. Segment(Z, A_1) → s_2
  69. Segment(A_1, A) → t_2
  70. LaTeX(f, true, true) → text1