MathPlotAI Logo MathPlotAI

Triangle Translation Demo

Triangle Translation Demo
Loading the math board and drawing, please wait…
2015-05-14 08:08
TriangleVectorCoordinate GeometryTransformation
This example demonstrates the transformation of a triangle through translation using vectors. Core math concepts include geometry transformations, coordinate geometry, and vectors. It utilizes commands like Intersect, Polygon, Rotate, Mirror, Vector, and Translate from GeoGebra. Ideal for high school students learning about geometric transformations and vectors.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Polygon(B, C, D) → poly1, d, b, c
  3. Rotate(B, α, A) → B'
  4. Rotate(C, α, A) → C'
  5. Rotate(D, α, A) → D'
  6. Polygon(B', C', D') → poly1', d', b', c'
  7. Rotate(B', α, A) → B''
  8. Rotate(C', α, A) → C''
  9. Rotate(D', α, A) → D''
  10. Polygon(B'', C'', D'') → poly1'', d'', b'', c''
  11. Rotate(B'', α, A) → B'''
  12. Rotate(C'', α, A) → C'''
  13. Rotate(D'', α, A) → D'''
  14. Polygon(B''', C''', D''') → poly1''', d''', b''', c'''
  15. Rotate(B''', α, A) → E
  16. Rotate(C''', α, A) → F
  17. Rotate(D''', α, A) → G
  18. Polygon(E, F, G) → poly2, g, e, f
  19. Mirror(B, yAxis) → B'_1
  20. Mirror(C, yAxis) → C'_1
  21. Mirror(D, yAxis) → D'_1
  22. Polygon(B'_1, C'_1, D'_1) → poly1'_1, d'_1, b'_1, c'_1
  23. Mirror(B', yAxis) → B''_1
  24. Mirror(C', yAxis) → C''_1
  25. Mirror(D', yAxis) → D''_1
  26. Polygon(B''_1, C''_1, D''_1) → poly1''_1, d''_1, b''_1, c''_1
  27. Mirror(B'', yAxis) → B'''_1
  28. Mirror(C'', yAxis) → C'''_1
  29. Mirror(D'', yAxis) → D'''_1
  30. Polygon(B'''_1, C'''_1, D'''_1) → poly1'''_1, d'''_1, b'''_1, c'''_1
  31. Mirror(B''', yAxis) → H
  32. Mirror(C''', yAxis) → I
  33. Mirror(D''', yAxis) → J
  34. Polygon(H, I, J) → poly3, j, h, i
  35. Mirror(E, yAxis) → E'
  36. Mirror(F, yAxis) → F'
  37. Mirror(G, yAxis) → G'
  38. Polygon(E', F', G') → poly2', g', e', f'
  39. Mirror(A, yAxis) → A'
  40. Vector(K, (x_4, y_4)) → u
  41. Translate(B, u) → B'_2
  42. Translate(C, u) → C'_2
  43. Translate(D, u) → D'_2
  44. Polygon(B'_2, C'_2, D'_2) → poly1'_2, d'_2, b'_2, c'_2
  45. Translate(B', u) → B''_2
  46. Translate(C', u) → C''_2
  47. Translate(D', u) → D''_2
  48. Polygon(B''_2, C''_2, D''_2) → poly1''_2, d''_2, b''_2, c''_2
  49. Translate(B'', u) → B'''_2
  50. Translate(C'', u) → C'''_2
  51. Translate(D'', u) → D'''_2
  52. Polygon(B'''_2, C'''_2, D'''_2) → poly1'''_2, d'''_2, b'''_2, c'''_2
  53. Translate(B''', u) → M
  54. Translate(C''', u) → N
  55. Translate(D''', u) → O
  56. Polygon(M, N, O) → poly4, o, m, n
  57. Translate(E, u) → E'_1
  58. Translate(F, u) → F'_1
  59. Translate(G, u) → G'_1
  60. Polygon(E'_1, F'_1, G'_1) → poly2'_1, g'_1, e'_1, f'_1
  61. Translate(B'_1, u) → P
  62. Translate(C'_1, u) → Q
  63. Translate(D'_1, u) → R
  64. Polygon(P, Q, R) → poly5, r, p, q
  65. Translate(B''_1, u) → S
  66. Translate(C''_1, u) → T
  67. Translate(D''_1, u) → U
  68. Polygon(S, T, U) → poly6, u_1, s, t
  69. Translate(B'''_1, u) → V
  70. Translate(C'''_1, u) → W
  71. Translate(D'''_1, u) → Z
  72. Polygon(V, W, Z) → poly7, z, v, w
  73. Translate(H, u) → H'
  74. Translate(I, u) → I'
  75. Translate(J, u) → J'
  76. Polygon(H', I', J') → poly3', j', h', i'
  77. Translate(E', u) → E''
  78. Translate(F', u) → F''
  79. Translate(G', u) → G''
  80. Polygon(E'', F'', G'') → poly2'', g'', e'', f''

AI Drawing Prompt Reference

Draw a triangle ABC, then rotate it three times around point A with angle α, followed by mirroring each vertex along the y-axis once, twice, and thrice respectively. Next, draw a new triangle EFG, then rotate it three times around point A with angle α, followed by mirroring each vertex along the y-axis once, and finally translating each vertex along vector u.
The prompt above was compiled from the original drawing commands and is for reference only.