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Glide-Reflections Activity

Glide-Reflections Activity
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2020-04-13 21:14
PolygonVectorTransformationGeometric ConstructionSlider Animation
This GeoGebra activity visually demonstrates how a glide reflection works, showing the composite transformation of a shape first translated along a line and then reflected across that same line. The core mathematical concepts include geometric transformations—translation, reflection, and their composition as a glide reflection—along with similarity transformations and symmetry. Construction highlights: the initial polygon (e.g., a rhombus) is created using the Polygon command; points and lines define the reflection axis; a Vector command establishes the translation vector; the Translate command performs the translation; the Mirror command applies the reflection; and the Distance command verifies corresponding distances. The object list includes multiple points (A through J, A13-A23, etc.) and auxiliary lines to track the pre-image and image. This activity is suitable for middle or high school geometry lessons on transformations, as well as introductory college geometry, helping learners grasp the essence of glide reflections and their relationship to translation and reflection.

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

AI Drawing Prompt Reference

Draw a polygon with ten vertices as the original shape. Pick a point on the x-axis and connect it to a fixed point to form a line as the reflection axis. Choose another point on this line to define a translation vector from the fixed point to that point. First translate every vertex of the original polygon by this vector to get a translated polygon. Then reflect the translated polygon across the line to obtain the final image. Also apply the same translation and reflection to another set of auxiliary points to show the combined transformation. Finally, measure the distance from a point on the original shape to the reflection axis to verify that corresponding distances remain unchanged.
The prompt above was compiled from the original drawing commands and is for reference only.