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探索平行线上的两次反射

探索平行线上的两次反射
几何画板及绘图内容加载中，请稍等……
2015-11-07 03:15
向量变换几何作图
所属专题 Glide Reflections Glide Reflections
这个范例展示了在平行线上进行两次反射的现象。核心数学概念包括反射变换和几何作图。通过使用Polygon, Line, Mirror, Distance, Intersect, OrthogonalLine, Midpoint等命令，可以构造出反射后的图形。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Polygon(A, B, C, D, E, F, G, H, I, J) → poly1, a, j, b, c, d, e, f, g, h, i
  2. Line(K, L) → Mirror1
  3. Mirror(A, Mirror1) → A'
  4. Mirror(B, Mirror1) → B'
  5. Mirror(C, Mirror1) → C'
  6. Mirror(D, Mirror1) → D'
  7. Mirror(E, Mirror1) → E'
  8. Mirror(F, Mirror1) → F'
  9. Mirror(G, Mirror1) → G'
  10. Mirror(H, Mirror1) → H'
  11. Mirror(I, Mirror1) → I'
  12. Mirror(J, Mirror1) → J'
  13. Polygon(A', B', C', D', E', F', G', H', I', J') → poly1'_1, a'_1, j'_1, b'_1, c'_1, d'_1, e'_1, f'_1, g'_1, h'_1, i'_1
  14. Mirror(A, Mirror1) → D16
  15. Mirror(B, Mirror1) → D17
  16. Mirror(C, Mirror1) → D18
  17. Mirror(D, Mirror1) → D19
  18. Mirror(E, Mirror1) → D20
  19. Mirror(F, Mirror1) → D21
  20. Mirror(G, Mirror1) → D22
  21. Mirror(H, Mirror1) → D23
  22. Mirror(I, Mirror1) → D24
  23. Mirror(J, Mirror1) → D25
  24. Distance(C, Mirror1) → l
  25. Distance(A, Mirror1) → B2
  26. Distance(B, Mirror1) → B3
  27. Distance(C, Mirror1) → B4
  28. Distance(D, Mirror1) → B5
  29. Distance(E, Mirror1) → B6
  30. Distance(F, Mirror1) → B7
  31. Distance(G, Mirror1) → B8
  32. Distance(H, Mirror1) → B9
  33. Distance(I, Mirror1) → B10
  34. Distance(J, Mirror1) → B11
  35. Distance(A', Mirror1) → D2
  36. Distance(B', Mirror1) → D3
  37. Distance(C', Mirror1) → D4
  38. Distance(D', Mirror1) → D5
  39. Distance(E', Mirror1) → D6
  40. Distance(F', Mirror1) → D7
  41. Distance(G', Mirror1) → D8
  42. Distance(H', Mirror1) → D9
  43. Distance(I', Mirror1) → D10
  44. Distance(J', Mirror1) → D11
  45. Line(M, Mirror1) → Mirror2
  46. Mirror(A', Mirror2) → A''
  47. Mirror(B', Mirror2) → B''
  48. Mirror(C', Mirror2) → C''
  49. Mirror(D', Mirror2) → D''
  50. Mirror(E', Mirror2) → E''
  51. Mirror(F', Mirror2) → F''
  52. Mirror(G', Mirror2) → G''
  53. Mirror(H', Mirror2) → H''
  54. Mirror(I', Mirror2) → I''
  55. Mirror(J', Mirror2) → J''
  56. Polygon(A'', B'', C'', D'', E'', F'', G'', H'', I'', J'') → poly2, a'', j'', b'', c'', d'', e'', f'', g'', h'', i''
  57. Distance(Mirror1, Mirror2) → n
  58. Distance(Mirror2, Mirror1) → o
  59. Intersect(Mirror1, yAxis) → N
  60. Distance(B24, C'') → distanceB24C''
  61. Distance(Mirror1, Mirror2) → p
  62. OrthogonalLine(N, Mirror2) → q
  63. Intersect(q, Mirror2) → O
  64. Distance(N, O) → distanceNO
  65. Midpoint(N, O) →
  66. Distance(B24, C'') → r
  67. Midpoint(B24, C'') →
  68. Distance(B19, H'') → distanceB19H''
  69. Midpoint(B19, H'') →
  70. Distance(N, O) → s
  71. Midpoint(N, O) →
  72. Distance(B17, J'') → distanceB17J''
  73. Midpoint(B17, J'') →
  74. Distance(B25, B'') → distanceB25B''
  75. Midpoint(B25, B'') →
  76. Distance(B19, H'') → t
  77. Midpoint(B19, H'') →