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Reflections Activity

Reflections Activity
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2020-04-03 20:34
Coordinate GeometryTransformationGeometric Construction
This example demonstrates the reflection transformation of points, lines, and polygons along lines, showing coordinate changes. Core math concepts include reflection, geometric transformations, coordinates, and vectors. It uses commands like Polygon, OrthogonalLine, Mirror, Line, Segment, and Angle in GeoGebra for construction. Suitable for middle school and above students learning geometric transformations and coordinate geometry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. Polygon(D, C, 4) → poly2, j, k, l, m, E, F
  3. Polygon(F, E, 4) → poly3, n, p, q, r, G, H
  4. Polygon(H, G, 4) → poly4, s, t, a, b, I, J
  5. Polygon(J, I, 4) → poly5, c, d, e, f_1, K, L
  6. Polygon(K, I, 4) → poly6, g_1, h_1, i_1, j_1, M, N
  7. Polygon(N, M, 4) → poly7, k_1, l_1, m_1, n_1, O, P
  8. Polygon(G, E, 4) → poly8, p_1, q_1, r_1, s_1, Q, R
  9. Polygon(A, L, P, O, I, G, R, Q, E, B) → poly9, a_1, b_1, l_2, p_2, o, i_2, g_2, r_2, q_2, e_1
  10. OrthogonalLine(T, xAxis) → f_2
  11. OrthogonalLine(S, yAxis) → h_2
  12. Mirror(A, f_2) → A'
  13. Mirror(L, f_2) → L'
  14. Mirror(P, f_2) → P'
  15. Mirror(O, f_2) → O'
  16. Mirror(I, f_2) → I'
  17. Mirror(G, f_2) → G'
  18. Mirror(R, f_2) → R'
  19. Mirror(Q, f_2) → Q'
  20. Mirror(E, f_2) → E'
  21. Mirror(B, f_2) → B'
  22. Polygon(A', L', P', O', I', G', R', Q', E', B') → poly9', a', b', l', p', o', i', g', r', q', e'
  23. Mirror(A, h_2) → A''
  24. Mirror(L, h_2) → L'_1
  25. Mirror(P, h_2) → P'_1
  26. Mirror(O, h_2) → O'_1
  27. Mirror(I, h_2) → I'_1
  28. Mirror(G, h_2) → G'_1
  29. Mirror(R, h_2) → R'_1
  30. Mirror(Q, h_2) → Q'_1
  31. Mirror(E, h_2) → E'_1
  32. Mirror(B, h_2) → B''
  33. Polygon(A'', L'_1, P'_1, O'_1, I'_1, G'_1, R'_1, Q'_1, E'_1, B'') → poly9'_1, a'_1, b'_1, l'_1, p'_1, o'_1, i'_1, g'_1, r'_1, q'_1, e'_1
  34. Mirror(A, t_1) → A'''
  35. Mirror(L, t_1) → L'_2
  36. Mirror(P, t_1) → P'_2
  37. Mirror(O, t_1) → O'_2
  38. Mirror(I, t_1) → I'_2
  39. Mirror(G, t_1) → G'_2
  40. Mirror(R, t_1) → R'_2
  41. Mirror(Q, t_1) → Q'_2
  42. Mirror(E, t_1) → E'_2
  43. Mirror(B, t_1) → B'''
  44. Polygon(A''', L'_2, P'_2, O'_2, I'_2, G'_2, R'_2, Q'_2, E'_2, B''') → poly9'_2, a'_2, b'_2, l'_2, p'_2, o'_2, i'_2, g'_2, r'_2, q'_2, e'_2
  45. Line(U, V) → j_2
  46. Mirror(A, j_2) → A''''
  47. Mirror(L, j_2) → L'_3
  48. Mirror(P, j_2) → P'_3
  49. Mirror(O, j_2) → O'_3
  50. Mirror(I, j_2) → I'_3
  51. Mirror(G, j_2) → G'_3
  52. Mirror(R, j_2) → R'_3
  53. Mirror(Q, j_2) → Q'_3
  54. Mirror(E, j_2) → E'_3
  55. Mirror(B, j_2) → B''''
  56. Polygon(A'''', L'_3, P'_3, O'_3, I'_3, G'_3, R'_3, Q'_3, E'_3, B'''') → poly9'_3, a'_3, b'_3, l'_3, p'_3, o'_3, i'_3, g'_3, r'_3, q'_3, e'_3
  57. Segment(B, B') → k_2
  58. Angle(k_2, f_2) → α
  59. Segment(B, B'') → m_2
  60. Angle(m_2, h_2) → β
  61. Segment(B, B''') → n_2
  62. Angle(n_2, t_1) → γ
  63. Segment(B, B'''') → s_2
  64. Angle(s_2, j_2) → δ

AI Drawing Prompt Reference

Draw a polygon with points A, L, P, O, I, G, R, Q, E, and B, then reflect it three times using the x-axis, y-axis, and line j2 to generate new polygons A', L', P', O', I', G', R', Q', E', and B', A'', L'_1, P'_1, O'_1, I'_1, G'_1, R'_1, Q'_1, E'_1, and B'', A''', L'_2, P'_2, O'_2, I'_2, G'_2, R'_2, Q'_2, E'_2, and B''' and show these reflected polygons.
The prompt above was compiled from the original drawing commands and is for reference only.