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Animation 5: Trapezoid Area Variation

Animation 5: Trapezoid Area Variation
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2016-06-14 21:23
PolygonCoordinate GeometryTransformation
This example demonstrates the variation of trapezoid area. Key mathematical concepts include the trapezoid area formula, slope, and standard deviation. Using GeoGebra commands such as Line, Ray, Point, Segment, Slope, PointIn, Midpoint, Dilate, Rotate, Polygon, etc., the deformation process of the trapezoid can be dynamically displayed. Suitable for high school mathematics education, particularly for coordinate geometry and function graphing.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Ray(A, B) → g
  3. Point(g) → C
  4. Ray(A, C) → h
  5. Segment(A, C) → i
  6. Slope(i) → m
  7. PointIn(a) → D
  8. Line(D, i) → j
  9. Point(j) → E
  10. Ray(D, E) → k
  11. Point(k) → F
  12. Segment(D, F) → l
  13. Segment(A, D) → n
  14. Segment(F, C) → p
  15. Midpoint(p) → G
  16. Dilate(A, If[0 < c ≤ 1, 1 - c, 0], C) → A'
  17. Segment(A, A') → q
  18. Dilate(C, If[1 < c ≤ 2, 2 - c, 0], G) → C'
  19. Segment(C, C') → r
  20. Dilate(G, If[2 < c ≤ 3, 3 - c, 0], F) → G'
  21. Segment(G, G') → s
  22. Rotate(C, If[3 < c ≤ 4, ((c - 3) * π), π], G) → C'_1
  23. Rotate(C', If[3 < c ≤ 4, ((c - 3) * π), π], G) → C''
  24. Segment(C'_1, C'') → r'
  25. Dilate(F, If[4 < c ≤ 5, 5 - c, 0], D) → F'
  26. Segment(F, F') → t
  27. Dilate(D, If[5 < c ≤ 6, 6 - c, 0], A) → D'
  28. Segment(D, D') → d
  29. Dilate(D, If[6.5 < c ≤ 7.5, 7.5 - c, 0], G) → D'_1
  30. Polygon(A, C, G, D) → poly1, a_1, c_1, g_1, d_1
  31. Polygon(G, F, D) → poly2, d_2, g_2, f_1
  32. Segment(D, D'_1) → e
  33. Rotate(G, If[8 < c ≤ 9, ((-(c - 8)) * π), π], G) → G'_1
  34. Rotate(F, If[8 < c ≤ 9, ((-(c - 8)) * π), π], G) → F'_1
  35. Rotate(D, If[8 < c ≤ 9, ((-(c - 8)) * π), π], G) → D'_2
  36. Polygon(G'_1, F'_1, D'_2) → poly2', d'_2, g'_1, f'_1
  37. Segment(F'_1, D'_2) → h_1
  38. Rotate(D, If[8 < c ≤ 9, ((-(c - 8)) * π), π], G) → D'_3
  39. Rotate(D'_1, If[8 < c ≤ 9, ((-(c - 8)) * π), π], G) → H
  40. Segment(D'_3, H) → e'
  41. Rotate(C'_1, If[8 < c ≤ 9, ((-(c - 8)) * π), π], G) → I
  42. Rotate(C'', If[8 < c ≤ 9, ((-(c - 8)) * π), π], G) → C'''
  43. Segment(I, C''') → r''
  44. OrthogonalLine(D, q) → i_1
  45. Intersect(f, q) → J
  46. Dilate(D, If[6 < c ≤ 7, 7 - c, 0], J) → D'_4
  47. Segment(D, D'_4) → j_1
  48. Min(t, q) → o
  49. Circle(J, (0.15 * o)) → e_1
  50. Intersect(e_1, i_1) → K, L
  51. Intersect(e_1, f) → M, N
  52. Angle(D, J, A) → α
  53. Angle(C, A, D) → β
  54. Intersect(i_1, f) → O
  55. Dilate(D, If[6 < c ≤ 7, 7 - c, 0], O) → D'_5
  56. Segment(D, D'_5) → k_1
  57. Angle(A, O, D) → γ
  58. Point(f) → P
  59. Point(f) → Q
  60. Circle(C, t) → p_1
  61. Intersect(p_1, f, 2) → R
  62. Ray(R, Q) → m_1
  63. Angle(F, C, A) → δ