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垂直线斜率旋转探索 by Tim Brzezinski

垂直线斜率旋转探索 by Tim Brzezinski
几何画板及绘图内容加载中，请稍等……
2016-07-14 09:03
角解析几何变换
所属专题 A1.ACE.1 - Create and solve equations and inequalities Expressing Geometric Properties with Equations (GPE) Cluster Parallel Lines and Planes Slope
本范例通过旋转三角形来探索坐标平面上垂直线的斜率关系。核心概念包括斜率、旋转和角度。使用了Circle, Rotate, Line, Intersect, OrthogonalLine, Segment, Dilate等GeoGebra命令。适合初中及以上学生进行几何探索和函数图像学习。

GeoGebra 命令及参数

  1. Circle(A, a_2) → c
  2. Rotate(B, α, A) → B'
  3. Line(A, B') → j
  4. Rotate(j, If[3.5 < b_1 ≤ 4.5, ((b_1 - 3.5) * π / 2), π / 2], A) → k
  5. Intersect(c, j, 2) → C
  6. OrthogonalLine(C, g) → h
  7. Intersect(g, h) → D
  8. Line(D, j) → i_1
  9. Intersect(k, i_1) → P
  10. Segment(C, D) → l
  11. Segment(A, D) → j_1
  12. Dilate(C, If[0 < b_1 ≤ 1, 1 - b_1, 0], D) → C'
  13. Segment(C, C') → b
  14. Min(b, j_1) → k_2
  15. Circle(D, (0.2 * k_2)) → e
  16. Intersect(e, l, 1) → F
  17. Angle(F, D, P) → δ
  18. Intersect(e, g, 2) → E
  19. CircleSector(D, E, F) → p
  20. Rotate(p, If[2 < b_1 ≤ 3, ((b_1 - 2) * π / 2), π / 2], D) → p'
  21. Angle(B, A, B') → β
  22. Polygon(A, D, C) → poly1, c_1, a_1, d
  23. Point(g) → G
  24. Ray(D, G) → m
  25. Point(m) → H
  26. Ray(D, H) → n
  27. Dilate(D, If[1 < b_1 ≤ 2, 2 - b_1, 0], A) → D'
  28. Segment(D, D') → a
  29. Ray(D, I) → i
  30. Intersect(e, i, 1) → J
  31. CircleSector(D, F, J) → q
  32. Circle(C, (0.2 * k_2)) → r
  33. Circle(A, (0.2 * k_2)) → s
  34. Intersect(s, j_1, 1) → K
  35. Intersect(s, j, 2) → L
  36. Intersect(r, l, 1) → M
  37. Intersect(r, j, 1) → N
  38. CircleSector(C, N, M) → t
  39. CircleSector(A, K, L) → d_1
  40. Rotate(q, If[2 < b_1 ≤ 3, ((-(b_1 - 2)) * π / 2), ((-π)) / 2], D) → q'
  41. CircleSector(C, M, N) → e_1
  42. CircleSector(A, L, K) → f_1
  43. Rotate(A, If[3.5 < b_1 ≤ 4.5, ((b_1 - 3.5) * π / 2), π / 2], A) → A'
  44. Rotate(D, If[3.5 < b_1 ≤ 4.5, ((b_1 - 3.5) * π / 2), π / 2], A) → D'_1
  45. Rotate(C, If[3.5 < b_1 ≤ 4.5, ((b_1 - 3.5) * π / 2), π / 2], A) → C'_1
  46. Polygon(A', D'_1, C'_1) → poly1', c'_1, a', d'_1
  47. Rotate(C, If[3.5 < b_1 ≤ 4.5, ((b_1 - 3.5) * π / 2), π / 2], A) → C'_2
  48. Rotate(C', If[3.5 < b_1 ≤ 4.5, ((b_1 - 3.5) * π / 2), π / 2], A) → C''
  49. Segment(C'_2, C'') → b'
  50. Rotate(D, If[3.5 < b_1 ≤ 4.5, ((b_1 - 3.5) * π / 2), π / 2], A) → D'_2
  51. Rotate(D', If[3.5 < b_1 ≤ 4.5, ((b_1 - 3.5) * π / 2), π / 2], A) → D''
  52. Segment(D'_2, D'') → a'_1
  53. Rotate(d_1, If[4.5 < b_1 ≤ 5.5, ((b_1 - 4.5) * π / 2), π / 2], A) → g_1
  54. CircleArc(A, K, L) → h_1
  55. Rotate(p', If[3.5 < b_1 ≤ 4.5, ((b_1 - 3.5) * π / 2), π / 2], A) → p''
  56. Rotate(t, If[5.5 < b_1 ≤ 6.5, ((-(b_1 - 5.5)) * π), (-π)], C) → t'
  57. CircleArc(C, N, M) → k_1
  58. Dilate(C, If[6.5 < b_1 ≤ 7.5, 7.5 - b_1, 0], A) → C'_3
  59. Vector(C, C'_3) → u
  60. Translate(t', u) → t''
  61. Dilate(D, If[9 < b_1 ≤ 10, 10 - b_1, 0], A) → D'_3
  62. Vector(D, D'_3) → v
  63. Rotate(p', If[8 < b_1 ≤ 9, ((b_1 - 8) * δ), δ], D) → p''_1
  64. Translate(p''_1, v) → p_1
  65. Point(k) → O
  66. Rotate(C, If[3.5 < b_1 ≤ 4.5, ((b_1 - 3.5) * π / 2), π / 2], A) → C'_4