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Geometric Transformations and Function Graphs Animation

Geometric Transformations and Function Graphs Animation
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2017-02-18 05:45
VectorDerivativeTransformationGeometric ConstructionGraphing
This example dynamically demonstrates the process of geometric transformations and function graphs through animation. It involves core mathematical concepts such as derivatives, function graphs, geometric transformations, and vector operations. Key GeoGebra commands and objects used in the construction include Line, Slope, PointIn, Segment, OrthogonalLine, Intersect, Point, Circle, Ray, Angle, Polygon, Dilate, Vector, and Translate. It is suitable for high school and above, focusing on learning dynamic demonstrations of function graphs, geometric transformations, and vector operations.

GeoGebra Commands & Parameters

  1. Line(A, B) → f_1
  2. Line(A, B) → b
  3. Slope(b) → m
  4. PointIn(d) → C
  5. Segment(A, B) → a
  6. Line(C, a) → f
  7. OrthogonalLine(B, f) → n
  8. Intersect(f, n) → H
  9. Segment(C, H) → l
  10. Point(l) → I
  11. OrthogonalLine(I, l) → q
  12. Intersect(q, a) → J
  13. Circle(B, Distance[A, J]) → g_1
  14. Intersect(g_1, f_1, 2) → M
  15. Segment(A, C) → e
  16. Point(f) → D
  17. Ray(C, D) → g
  18. Line(B, e) → h
  19. Intersect(h, g) → E
  20. Segment(C, E) → i
  21. Segment(B, E) → j
  22. Point(i) → F
  23. OrthogonalLine(A, i) → k
  24. Angle(B, A, C) → α
  25. Ray(C, E) → p
  26. Intersect(f, k) → G
  27. Segment(G, E) → r
  28. Point(r) → K
  29. OrthogonalLine(K, r) → s
  30. Intersect(s, a) → L
  31. Polygon(A, J, I, C) → poly1, a_1, j_1, i_1, c_1
  32. Polygon(J, B, E, I) → poly2, j_2, b_1, e_1, i_2
  33. Polygon(A, L, K, C) → poly3, a_2, l_1, k_1, c_2
  34. Polygon(L, B, E, K) → poly4, l_2, b_2, e_2, k_2
  35. Dilate(I, If[0 < o ≤ 1, 1 - o, 0], J) → I'
  36. Segment(I, I') → t
  37. Angle(J, I, E) → β
  38. Dilate(J, If[2 < o ≤ 3, 3 - o, 0], M) → J'
  39. Vector(J, J') → u
  40. Angle(B, J, I) → γ
  41. OrthogonalLine(E, b) → d_1
  42. Translate(A, u) → A'
  43. Translate(J, u) → J'_1
  44. Translate(I, u) → I'_1
  45. Translate(C, u) → C'
  46. Polygon(A', J'_1, I'_1, C') → poly1', a', j'_1, i'_1, c'
  47. Angle(I'_1, J', J) → δ
  48. Polygon(A, B, E, C) → poly5, a_3, b_3, e_3, c_3
  49. Circle(E, Distance[C, K]) → h_1
  50. Intersect(h_1, f, 2) → N
  51. Polygon(A, B, E, C) → poly6, a_4, b_4, e_4, c_4
  52. Dilate(K, If[0 < o ≤ 1, 1 - o, 0], L) → K'
  53. Segment(K, K') → m_1
  54. Angle(L, K, E) → ε
  55. Angle(B, L, K) → ζ
  56. Dilate(K, If[2 < o ≤ 3, 3 - o, 0], N) → K'_1
  57. Vector(K, K'_1) → v
  58. Translate(A, v) → A'_1
  59. Translate(L, v) → L'
  60. Translate(K, v) → K'_2
  61. Translate(C, v) → C'_1
  62. Polygon(A'_1, L', K'_2, C'_1) → poly3', a'_1, l', k'_2, c'_1
  63. Angle(K'_1, L', A) → η