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Two Reflections by Roy Wright

Two Reflections by Roy Wright
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2014-06-17 23:42
VectorTransformationGeometric Construction
This example demonstrates how two consecutive line reflections can be used to create any desired translation and/or rotation. It involves core math concepts like reflection, rotation, translation, vector, and geometric construction. Constructed using GeoGebra commands: Segment, Line, Mirror. Suitable for high school geometry transformation teaching, math competitions, and geometric exploration activities.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Segment(B, C) → b
  3. Segment(C, A) → c
  4. Line(D, E) → d
  5. Line(F, G) → e
  6. Line(H, I) → f
  7. Mirror(B, d) → B'
  8. Mirror(C, d) → C'
  9. Segment(B', C') → b'
  10. Mirror(A, d) → A'
  11. Mirror(B, d) → B'_1
  12. Segment(A', B'_1) → a'
  13. Mirror(C, d) → C'_1
  14. Mirror(A, d) → A'_1
  15. Segment(C'_1, A'_1) → c'
  16. Mirror(B', e) → B''
  17. Mirror(C', e) → C''
  18. Segment(B'', C'') → b''
  19. Mirror(C'_1, e) → J
  20. Mirror(A'_1, e) → K
  21. Segment(J, K) → c''
  22. Mirror(A', e) → A''
  23. Mirror(B'_1, e) → L
  24. Segment(A'', L) → a''
  25. Mirror(J, f) → J'
  26. Mirror(K, f) → K'
  27. Segment(J', K') → c'''
  28. Mirror(A'', f) → A'''
  29. Mirror(L, f) → L'
  30. Segment(A''', L') → a'''
  31. Mirror(B'', f) → B'''
  32. Mirror(C'', f) → C'''
  33. Segment(B''', C''') → b'''
  34. Segment(A_2, B_2) → a_2
  35. Segment(B_2, C_2) → b_2
  36. Segment(C_2, A_2) → c_2
  37. Segment(A_3, B_3) → a_3
  38. Segment(B_3, C_3) → b_3
  39. Segment(C_3, A_3) → c_3
  40. Line(N, O) → g
  41. Line(O, P) → h
  42. Mirror(A, g) → A'_2
  43. Mirror(B, g) → B'_2
  44. Segment(A'_2, B'_2) → a'_1
  45. Mirror(B, g) → B'_3
  46. Mirror(C, g) → C'_2
  47. Segment(B'_3, C'_2) → b'_1
  48. Mirror(C, g) → C'_3
  49. Mirror(A, g) → A'_3
  50. Segment(C'_3, A'_3) → c'_1
  51. Mirror(A'_2, h) → Q
  52. Mirror(B'_2, h) → R
  53. Segment(Q, R) → i
  54. Mirror(B'_3, h) → S
  55. Mirror(C'_2, h) → T
  56. Segment(S, T) → j
  57. Mirror(C'_3, h) → U
  58. Mirror(A'_3, h) → V
  59. Segment(U, V) → k
  60. Line(M, W) → l
  61. Line(Z, l) → m
  62. Mirror(A, l) → A'_4
  63. Mirror(B, l) → B'_4
  64. Segment(A'_4, B'_4) → a'_2
  65. Mirror(B, l) → B'_5
  66. Mirror(C, l) → C'_4
  67. Segment(B'_5, C'_4) → b'_2
  68. Mirror(C, l) → C'_5
  69. Mirror(A, l) → A'_5
  70. Segment(C'_5, A'_5) → c'_2
  71. Mirror(A'_4, m) → D_1
  72. Mirror(B'_4, m) → E_1
  73. Segment(D_1, E_1) → n
  74. Mirror(B'_5, m) → F_1
  75. Mirror(C'_4, m) → G_1
  76. Segment(F_1, G_1) → p
  77. Mirror(C'_5, m) → H_1
  78. Mirror(A'_5, m) → I_1
  79. Segment(H_1, I_1) → q

AI Drawing Prompt Reference

Draw a triangle and three lines. Reflect the two sides of the triangle successively with the first line to get two new points, and connect them to form a new line segment. Reflect all vertices of the triangle with the first line to get three new points, and connect them to form three new line segments. Then reflect the two new line segments with the second line to get two new sets of points, and connect them to form four new line segments. Finally, reflect the four new line segments with the third line to get two new sets of points, and connect them to form eight new line segments.
The prompt above was compiled from the original drawing commands and is for reference only.