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Exploring Two Reflections with Parallel Lines

Exploring Two Reflections with Parallel Lines
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2015-11-07 03:15
VectorTransformationGeometric Construction
In collections Glide Reflections Glide Reflections
This example demonstrates the phenomenon of two reflections on parallel lines. Key mathematical concepts include reflection transformations and geometric construction. Using commands like Polygon, Line, Mirror, Distance, Intersect, OrthogonalLine, and Midpoint, the reflected shapes can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D, E, F, G, H, I, J) → poly1, a, j, b, c, d, e, f, g, h, i
  2. Line(K, L) → Mirror1
  3. Mirror(A, Mirror1) → A'
  4. Mirror(B, Mirror1) → B'
  5. Mirror(C, Mirror1) → C'
  6. Mirror(D, Mirror1) → D'
  7. Mirror(E, Mirror1) → E'
  8. Mirror(F, Mirror1) → F'
  9. Mirror(G, Mirror1) → G'
  10. Mirror(H, Mirror1) → H'
  11. Mirror(I, Mirror1) → I'
  12. Mirror(J, Mirror1) → J'
  13. Polygon(A', B', C', D', E', F', G', H', I', J') → poly1'_1, a'_1, j'_1, b'_1, c'_1, d'_1, e'_1, f'_1, g'_1, h'_1, i'_1
  14. Mirror(A, Mirror1) → D16
  15. Mirror(B, Mirror1) → D17
  16. Mirror(C, Mirror1) → D18
  17. Mirror(D, Mirror1) → D19
  18. Mirror(E, Mirror1) → D20
  19. Mirror(F, Mirror1) → D21
  20. Mirror(G, Mirror1) → D22
  21. Mirror(H, Mirror1) → D23
  22. Mirror(I, Mirror1) → D24
  23. Mirror(J, Mirror1) → D25
  24. Distance(C, Mirror1) → l
  25. Distance(A, Mirror1) → B2
  26. Distance(B, Mirror1) → B3
  27. Distance(C, Mirror1) → B4
  28. Distance(D, Mirror1) → B5
  29. Distance(E, Mirror1) → B6
  30. Distance(F, Mirror1) → B7
  31. Distance(G, Mirror1) → B8
  32. Distance(H, Mirror1) → B9
  33. Distance(I, Mirror1) → B10
  34. Distance(J, Mirror1) → B11
  35. Distance(A', Mirror1) → D2
  36. Distance(B', Mirror1) → D3
  37. Distance(C', Mirror1) → D4
  38. Distance(D', Mirror1) → D5
  39. Distance(E', Mirror1) → D6
  40. Distance(F', Mirror1) → D7
  41. Distance(G', Mirror1) → D8
  42. Distance(H', Mirror1) → D9
  43. Distance(I', Mirror1) → D10
  44. Distance(J', Mirror1) → D11
  45. Line(M, Mirror1) → Mirror2
  46. Mirror(A', Mirror2) → A''
  47. Mirror(B', Mirror2) → B''
  48. Mirror(C', Mirror2) → C''
  49. Mirror(D', Mirror2) → D''
  50. Mirror(E', Mirror2) → E''
  51. Mirror(F', Mirror2) → F''
  52. Mirror(G', Mirror2) → G''
  53. Mirror(H', Mirror2) → H''
  54. Mirror(I', Mirror2) → I''
  55. Mirror(J', Mirror2) → J''
  56. Polygon(A'', B'', C'', D'', E'', F'', G'', H'', I'', J'') → poly2, a'', j'', b'', c'', d'', e'', f'', g'', h'', i''
  57. Distance(Mirror1, Mirror2) → n
  58. Distance(Mirror2, Mirror1) → o
  59. Intersect(Mirror1, yAxis) → N
  60. Distance(B24, C'') → distanceB24C''
  61. Distance(Mirror1, Mirror2) → p
  62. OrthogonalLine(N, Mirror2) → q
  63. Intersect(q, Mirror2) → O
  64. Distance(N, O) → distanceNO
  65. Midpoint(N, O) →
  66. Distance(B24, C'') → r
  67. Midpoint(B24, C'') →
  68. Distance(B19, H'') → distanceB19H''
  69. Midpoint(B19, H'') →
  70. Distance(N, O) → s
  71. Midpoint(N, O) →
  72. Distance(B17, J'') → distanceB17J''
  73. Midpoint(B17, J'') →
  74. Distance(B25, B'') → distanceB25B''
  75. Midpoint(B25, B'') →
  76. Distance(B19, H'') → t
  77. Midpoint(B19, H'') →