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Exploring Glide-Reflections by Brittany Wilson

Exploring Glide-Reflections by Brittany Wilson
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2015-11-09 08:29
Coordinate GeometryTransformationGeometric Construction
This example demonstrates the concept of glide-reflection, a combination of translation and reflection, in geometry. It involves core math concepts like reflections, straight lines, polygon construction, vector operations, and distance calculations. The construction uses GeoGebra commands such as Polygon, Point, Line, Vector, Translate, Mirror, and Distance. Ideal for high school coordinate geometry lessons or math clubs exploring transformations.

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. Point(xAxis) → K
  3. Line(P, K) → m
  4. Point(m) → Q
  5. Vector(P, Q) → z
  6. Translate(A, z) → A'_1
  7. Translate(B, z) → B'_1
  8. Translate(C, z) → C'_1
  9. Translate(D, z) → D'_1
  10. Translate(E, z) → E'_1
  11. Translate(F, z) → F'_1
  12. Translate(G, z) → G'_1
  13. Translate(H, z) → H'_1
  14. Translate(I, z) → I'_1
  15. Translate(J, z) → J'_1
  16. Polygon(A'_1, B'_1, C'_1, D'_1, E'_1, F'_1, G'_1, H'_1, I'_1, J'_1) → poly1', a', j', b', c', d', e', f', g', h', i'
  17. Translate(B14, z) → A'
  18. Translate(B15, z) → B'
  19. Translate(B16, z) → C'
  20. Translate(B17, z) → D'
  21. Translate(B18, z) → E'
  22. Translate(B19, z) → F'
  23. Translate(B20, z) → G'
  24. Translate(B21, z) → H'
  25. Translate(B22, z) → I'
  26. Translate(B23, z) → J'
  27. Mirror(A'_1, m) → A''_1
  28. Mirror(B'_1, m) → B''_1
  29. Mirror(C'_1, m) → C''_1
  30. Mirror(D'_1, m) → D''_1
  31. Mirror(E'_1, m) → E''_1
  32. Mirror(F'_1, m) → F''_1
  33. Mirror(G'_1, m) → G''_1
  34. Mirror(H'_1, m) → H''_1
  35. Mirror(I'_1, m) → I''_1
  36. Mirror(J'_1, m) → J''_1
  37. Polygon(A''_1, B''_1, C''_1, D''_1, E''_1, F''_1, G''_1, H''_1, I''_1, J''_1) → poly1'', a'', j'', b'', c'', d'', e'', f'', g'', h'', i''
  38. Mirror(A', m) → A''
  39. Mirror(B', m) → B''
  40. Mirror(C', m) → C''
  41. Mirror(D', m) → D''
  42. Mirror(E', m) → E''
  43. Mirror(F', m) → F''
  44. Mirror(G', m) → G''
  45. Mirror(H', m) → H''
  46. Mirror(I', m) → I''
  47. Mirror(J', m) → J''
  48. Distance(A, m) → B2
  49. Distance(B, m) → B3
  50. Distance(C, m) → B4
  51. Distance(D, m) → B5
  52. Distance(E, m) → B6
  53. Distance(F, m) → B7
  54. Distance(G, m) → B8
  55. Distance(H, m) → B9
  56. Distance(I, m) → B10
  57. Distance(J, m) → B11
  58. Distance(A', m) → D2
  59. Distance(B', m) → D3
  60. Distance(C', m) → D4
  61. Distance(D', m) → D5
  62. Distance(E', m) → D6
  63. Distance(F', m) → D7
  64. Distance(G', m) → D8
  65. Distance(H', m) → D9
  66. Distance(I', m) → D10
  67. Distance(J', m) → D11
  68. Distance(A'', m) → F2
  69. Distance(B'', m) → F3
  70. Distance(C'', m) → F4
  71. Distance(D'', m) → F5
  72. Distance(E'', m) → F6
  73. Distance(F'', m) → F7
  74. Distance(G'', m) → F8
  75. Distance(H'', m) → F9
  76. Distance(I'', m) → F10
  77. Distance(J'', m) → F11
  78. Translate(A, z) → D14
  79. Translate(B, z) → D15
  80. Translate(C, z) → E16_1
  81. Translate(C, z) → D16
  82. Translate(D, z) → D17
  83. Translate(E, z) → D18
  84. Translate(F, z) → D19
  85. Translate(G, z) → D20
  86. Translate(H, z) → D21
  87. Translate(I, z) → D22
  88. Translate(J, z) → D23
  89. Mirror(A', m) → F14
  90. Mirror(B', m) → F15
  91. Mirror(C', m) → F16
  92. Mirror(D', m) → F17
  93. Mirror(E', m) → F18
  94. Mirror(F', m) → F19
  95. Mirror(G', m) → F20
  96. Mirror(H', m) → F21
  97. Mirror(I', m) → F22
  98. Mirror(J', m) → F23
  99. Distance(P, Q) → distancePQ