等距变换

等距变换
几何画板及绘图内容加载中,请稍等……
2017-12-25 10:15
所属专题 Mathematics Form 2
这个范例演示了等距变换的概念。等距变换包括平移、旋转、反射和滑动。通过使用GeoGebra命令如Translate、Rotate、Mirror和Shear,可以直观地展示这些变换如何保持图形的大小和形状不变。适合初中及以上学生学习几何变换。

GeoGebra 命令及参数

  1. SelectedIndex(Bahasa) → nn
  2. Polygon(A, B, C) → poly1, c, a, b
  3. PointIn(poly1) → P
  4. PointIn(poly1) → Q
  5. If(nn ≟ 1, {"Translation", "Reflection", "Rotation", "Transformation 4", "Transformation 5", "Transformation 6"}, {"Translasi", "Pantulan", "Putaran", "Transformasi 4", "Transformasi 5", "Transformasi 6"}) → Transform
  6. SelectedIndex(Transform) → m
  7. Vector(G, H) → u
  8. Translate(A, u) → A'
  9. Translate(B, u) → B'
  10. Translate(C, u) → C'
  11. Polygon(A', B', C') → poly1', c', a', b'
  12. Translate(P, u) → P'
  13. Translate(Q, u) → Q'
  14. Line(D, E) → f
  15. Mirror(A, f) → A'_1
  16. Mirror(B, f) → B'_1
  17. Mirror(C, f) → C'_1
  18. Polygon(A'_1, B'_1, C'_1) → poly1'_1, c'_1, a'_1, b'_1
  19. Mirror(P, f) → P'_1
  20. Mirror(Q, f) → Q'_1
  21. Rotate(A, Ar°, F) → A'_2
  22. Rotate(B, Ar°, F) → B'_2
  23. Rotate(C, Ar°, F) → C'_2
  24. Polygon(A'_2, B'_2, C'_2) → poly1'_2, c'_2, a'_2, b'_2
  25. Rotate(P, Ar°, F) → P'_2
  26. Rotate(Q, Ar°, F) → Q'_2
  27. Dilate(A, Sf, K) → A'_3
  28. Dilate(B, Sf, K) → B'_3
  29. Dilate(C, Sf, K) → C'_3
  30. Polygon(A'_3, B'_3, C'_3) → poly1'_3, c'_3, a'_3, b'_3
  31. Dilate(P, Sf, K) → P'_3
  32. Dilate(Q, Sf, K) → Q'_3
  33. Line(L, M) → g
  34. Shear(A, g, Sr) → A'_4
  35. Shear(B, g, Sr) → B'_4
  36. Shear(C, g, Sr) → C'_4
  37. Polygon(A'_4, B'_4, C'_4) → poly1'_4, c'_4, a'_4, b'_4
  38. Shear(P, g, Sr) → P'_4
  39. Shear(Q, g, Sr) → Q'_4
  40. Line(I, J) → h
  41. Stretch(A, h, Str) → A'_5
  42. Stretch(B, h, Str) → B'_5
  43. Stretch(C, h, Str) → C'_5
  44. Polygon(A'_5, B'_5, C'_5) → poly1'_5, c'_5, a'_5, b'_5
  45. Stretch(P, h, Str) → P'_5
  46. Stretch(Q, h, Str) → Q'_5
  47. Segment(G, H) → i
  48. Circle(H, 0.3) → d
  49. Intersect(d, i, 1) → N
  50. Rotate(N, 30°, H) → N'
  51. Rotate(N, (-(30°)), H) → N'_1
  52. Segment(H, N'_1) → j
  53. Segment(H, N') → k
  54. Distance(P, Q) → OD
  55. Segment(Q, P) → l
  56. Segment(P', Q') → n
  57. Segment(P'_1, Q'_1) → p
  58. Segment(P'_2, Q'_2) → q
  59. Segment(P'_3, Q'_3) → r
  60. Segment(P'_4, Q'_4) → s
  61. Segment(P'_5, Q'_5) → t
  62. If(nn ≟ 1, "Distance ", "Jarak ") → Tex1
  63. If(nn ≟ 1, If[OD ≤ 1, " unit", " units"], " unit") → Tex2
  64. If(nn ≟ 1, If[Jr ≤ 1, " unit", " units"], " unit") → Tex3

AI 绘图提示语参考

绘制一个三角形ABC,然后依次进行平移、反射、旋转、仿射变换和伸缩变换,每种变换后生成新的三角形,并将变换前后的点也显示出来。首先平移三角形ABC到A'B'C',然后反射到A'_1B'_1C'_1,接着旋转到A'_2B'_2C'_2,再进行仿射变换到A'_4B'_4C'_4,最后伸缩变换到A'_5B'_5C'_5。
以上提示语为根据原始绘图命令整理而来,仅供参考。