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Hyperbola Reflections

Hyperbola Reflections
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2016-02-15 08:26
VectorFunctionCoordinate GeometryTransformationGeometric Construction
This example demonstrates the reflection of a hyperbola. Key mathematical concepts include hyperbola, reflection, vectors, and geometric construction. Using GeoGebra commands such as Line, Segment, Intersect, Tangent, OrthogonalLine, Mirror, etc., the symmetry of the hyperbola is visually illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  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