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平行四边形面积计算 by Ooi Soo Huat (2)

平行四边形面积计算 by Ooi Soo Huat (2)
几何画板及绘图内容加载中，请稍等……
2017-12-11 14:36
向量解析几何几何作图
所属专题 Mathematics Form 1
①本范例演示如何通过向量法计算平行四边形面积；②涉及核心概念：向量、向量叉积、几何作图；③构造要点：使用Line, Point, Vector, Polygon等命令绘制平行四边形并计算向量叉积模长；④适合高中数学学生及需要理解向量应用的初学者。

GeoGebra 命令及参数

  1. Line(A, yAxis) → b
  2. Line(A, xAxis) → a
  3. Point(a) → B
  4. Distance(A, B) → AB
  5. Line(B, b) → c
  6. Point(c) → C
  7. Line(C, a) → d
  8. Point(d) → G
  9. Intersect(b, d) → D
  10. If(NearC ≟ true, C, G) → Pm
  11. DynamicCoordinates(G, x(Pm), y(Pm)) → E
  12. Line(E, c) → g
  13. Intersect(a, g) → H
  14. Circle(E, AB) → e
  15. Intersect(e, d, 1) → F
  16. Line(F, b) → h
  17. Intersect(a, h) → I
  18. Distance(C, E) → EC
  19. Distance(E, H) → EH
  20. If(E_B ≟ true, Polygon[E, B, H], Polygon[E, B, C]) → poly1
  21. Polygon(I, B, C, F) → poly2, i, b_2, c_2, f
  22. If(E_B ≟ true, Polygon[F, A, D], Polygon[F, A, I]) → poly3
  23. Polygon(A, H, E, D) → poly4, a_1, h_1, e_1, d_1
  24. Polygon(A, B, C, D) → poly5, a_2, b_1, c_1, d_2
  25. Vector(C, D) → u
  26. If(E_R ≟ true, Translate[poly1, Vector[(m * u)]], Translate[poly3, Vector[(m * (-u))]]) → Trans
  27. Midpoint(D, A) → J
  28. Line(J, a) → j
  29. Circle(J, n) → k
  30. Intersect(k, j, 1) → K
  31. Line(K, h) → l
  32. Circle(K, n) → p
  33. Intersect(p, l, 2) → L
  34. Intersect(p, l, 1) → M
  35. Intersect(d, l) → N
  36. Intersect(a, l) → O
  37. Vector(M, O) → v
  38. Vector(L, N) → w
  39. Midpoint(A, B) → P
  40. Circle(P, n) → q
  41. Line(P, c) → r
  42. Intersect(q, r, 1) → Q
  43. Line(Q, j) → s
  44. Circle(Q, n) → t
  45. Intersect(t, s, 1) → R
  46. Intersect(t, s, 2) → S
  47. Intersect(c, s) → T
  48. Intersect(b, s) → U
  49. Vector(R, U) → u_1
  50. Vector(S, T) → v_1
  51. Intersect(j, c) → V
  52. Circle(V, n) → f_1
  53. Intersect(f_1, c) → W, Z
  54. Segment(D, C) → k_1
  55. Segment(C, B) → l_1
  56. Segment(B, A) → m_1
  57. Intersect(f_1, j, 2) → A_1
  58. Line(A_1, r) → g_1
  59. Circle(A_1, n) → p_1
  60. Intersect(p_1, g_1, 2) → B_1
  61. Intersect(p_1, g_1, 1) → C_1
  62. Intersect(d, g_1) → D_1
  63. Intersect(a, g_1) → E_1
  64. Vector(B_1, D_1) → w_1
  65. Vector(C_1, E_1) → i_1
  66. Segment(A, D) → j_1
  67. Angle(A, D, C) → α
  68. Angle(C, B, A) → β
  69. SelectedIndex(Bahasa) → nn
  70. If(nn ≟ 1, "Derive the formula to calculate", "Menerbit rumus untuk menghitungkan") → Tex1
  71. If(nn ≟ 1, "the area of a parallelogram", "luas bentuk segi empat selari") → Tex2