MathPlotAI Logo MathPlotAI

Reflections and Translations by Sonia Cintron

Reflections and Translations by Sonia Cintron
Loading the math board and drawing, please wait…
2016-12-13 07:32
TriangleVectorTransformationGeometric Construction
This example demonstrates reflections and translations of triangles, involving core math concepts like reflection, translation, vector, and polygon construction. It uses commands like Polygon, Vector, Translate, Point, Line, Mirror, Segment in GeoGebra. Suitable for high school mathematics teaching to understand the properties of geometric transformations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Vector(C, D) → u
  3. Translate(A, u) → A'
  4. Translate(B, u) → B'
  5. Translate(C, u) → C'
  6. Polygon(A', B', C') → poly1', c', a', b'
  7. Point(u) → E
  8. Vector(C, E) → v
  9. Translate(A, v) → A'_1
  10. Translate(B, v) → B'_1
  11. Translate(C, v) → C'_1
  12. Polygon(A'_1, B'_1, C'_1) → poly1'_1, c'_1, a'_1, b'_1
  13. Line(D, F) → d
  14. Mirror(A', d) → A''
  15. Mirror(B', d) → B''
  16. Mirror(C', d) → C''
  17. Polygon(A'', B'', C'') → poly1'', c'', a'', b''
  18. Mirror(A'_1, d) → G
  19. Mirror(B'_1, d) → H
  20. Mirror(C'_1, d) → I
  21. Polygon(G, H, I) → poly2, i, g, h
  22. Mirror(A, d) → A'_2
  23. Mirror(B, d) → B'_2
  24. Mirror(C, d) → C'_2
  25. Polygon(A'_2, B'_2, C'_2) → poly1'_2, c'_2, a'_2, b'_2
  26. Line(J, d) → e
  27. Vector(J, K) → w
  28. Mirror(A'_1, e) → L
  29. Mirror(B'_1, e) → M
  30. Mirror(C'_1, e) → N
  31. Point(w) → O
  32. Vector(J, O) → z
  33. Translate(L, f) → L'
  34. Translate(M, f) → M'
  35. Translate(N, f) → N'
  36. Translate(L', z) → L''
  37. Translate(M', z) → M''
  38. Translate(N', z) → N''
  39. Translate(A'_2, z) → P
  40. Translate(B'_2, z) → Q
  41. Translate(C'_2, z) → R
  42. Mirror(A, e) → A'_3
  43. Mirror(B, e) → B'_3
  44. Mirror(C, e) → C'_3
  45. Polygon(A'_3, B'_3, C'_3) → poly1'_3, c'_3, a'_3, b'_3
  46. Translate(A'_3, z) → S
  47. Translate(B'_3, z) → T
  48. Translate(C'_3, z) → U
  49. Polygon(S, T, U) → poly3, u_1, s, t
  50. Segment(E, D) → j
  51. Mirror(A'_1, d) → V
  52. Mirror(B'_1, d) → W
  53. Mirror(C'_1, d) → Z
  54. Polygon(V, W, Z) → poly4, z_1, v_1, w_1
  55. Vector(A_1, D) → k
  56. Mirror(E, d) → E'
  57. Segment(E', D) → l
  58. Vector(C'_3, D) → m
  59. Segment(A, B) → n
  60. Segment(B, C) → p
  61. Segment(C, A) → q
  62. Translate(C, w) → C'_4
  63. Vector(C, C'_4) → r
  64. Point(r) → B_1
  65. Vector(C, B_1) → a_1
  66. Translate(A, a_1) → A'_4
  67. Translate(B, a_1) → B'_4
  68. Translate(C, a_1) → C'_5
  69. Polygon(A'_4, B'_4, C'_5) → poly1'_4, c'_5, a'_4, b'_4
  70. Segment(B_1, C'_4) → b_1
  71. Translate(A, r) → A'_5
  72. Translate(B, r) → B'_5
  73. Segment(A'_5, B'_5) → n'
  74. Translate(B, r) → B'_6
  75. Translate(C, r) → C'_6
  76. Segment(B'_6, C'_6) → p'
  77. Translate(C, r) → C'_7
  78. Translate(A, r) → A'_6
  79. Segment(C'_7, A'_6) → q'
  80. Mirror(A'_4, e) → C_1
  81. Mirror(B'_4, e) → D_1
  82. Mirror(C'_5, e) → E_1
  83. Polygon(C_1, D_1, E_1) → poly5, e_1, c_1, d_1
  84. Segment(E, D) → f_1
  85. Line(M_1, N_1) → g_1
  86. Segment(O, K) → h_1