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反射与平移

反射与平移
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2016-12-13 07:32
测试改名0向量变换几何作图
①本范例演示了三角形的反射与平移变换；②涉及的核心数学概念包括反射、平移、向量、多边形构造；③作图要点——使用了Polygon、Vector、Translate、Point、Line、Mirror、Segment等GeoGebra命令与对象；④适合高中数学教学，用于理解几何变换的性质。

GeoGebra 命令及参数

  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