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Geometric Transformations and Optimization Animation

Geometric Transformations and Optimization Animation
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2017-03-02 19:20
FunctionTrigonometryCoordinate GeometryOptimizationGeometric Construction
This example demonstrates geometric transformations involving triangles and circles through animation, integrating function graphs to analyze angles and optimization problems. Core concepts include geometric transformations (scaling, rotation), coordinate geometry, function optimization, and problem-solving. Construction uses commands like Line, Point, Circle, Dilate, Segment, Intersect, Polygon, with key steps involving dilation for transformations and intersection for finding points. Suitable for high school and above, focusing on geometric transformations, function optimization, and coordinate geometry applications.

GeoGebra Commands & Parameters

  1. Line(A_1, A') → f
  2. Line(A_1, C') → g
  3. Line(A_1, B') → h
  4. Point(g) → C
  5. Point(g) → C'_1
  6. Point(f) → A'_1
  7. Point(f) → A
  8. Point(h) → B
  9. Point(h) → B'_1
  10. Circle(A'_1, 1) → r
  11. Circle(A, 1) → t
  12. Dilate(A_1, If[0 < a ≤ 1, 1 - a, 0], A) → N
  13. Dilate(A_1, If[0 < a ≤ 1, 1 - a, 0], A') → O
  14. Segment(A_1, N) → b
  15. Segment(A_1, O) → i_1
  16. Dilate(A_1, If[1 < a ≤ 2, 2 - a, 0], B') → P
  17. Dilate(A_1, If[1 < a ≤ 2, 2 - a, 0], B) → Q
  18. Segment(A_1, P) → l_1
  19. Segment(A_1, Q) → m_1
  20. Dilate(A_1, If[2 < a ≤ 3, 3 - a, 0], C') → H
  21. Dilate(A_1, If[2 < a ≤ 3, 3 - a, 0], C) → I
  22. Segment(A_1, H) → c
  23. Segment(A_1, I) → d
  24. Line(A', B') → j
  25. Line(B, A) → k
  26. Intersect(j, k) → D
  27. Line(C', B') → l
  28. Line(B, C) → m
  29. Intersect(l, m) → E
  30. Line(C', A') → n
  31. Line(A, C) → p
  32. Intersect(n, p) → F
  33. Polygon(A, C, B) → poly1, b_1, a_1, c_1
  34. Polygon(A', B', C') → poly3, c', a', b'
  35. Dilate(B, If[5 < a ≤ 6, 6 - a, 0], D) → B'_2
  36. Segment(B, B'_2) → i
  37. Dilate(A', If[5 < a ≤ 6, 6 - a, 0], D) → A''
  38. Segment(A', A'') → q
  39. Dilate(B, If[6 < a ≤ 7, 7 - a, 0], E) → B'_3
  40. Dilate(C', If[6 < a ≤ 7, 7 - a, 0], E) → C''
  41. Segment(B, B'_3) → s
  42. Segment(C', C'') → e
  43. Dilate(A, If[7 < a ≤ 8, 8 - a, 0], F) → A'_2
  44. Dilate(C', If[7 < a ≤ 8, 8 - a, 0], F) → C''_1
  45. Segment(C', C''_1) → f_1
  46. Segment(A, A'_2) → g_1
  47. Dilate(D, If[10 < a ≤ 11, 11 - a, 0], E) → D'
  48. Dilate(E, If[11 < a ≤ 12, 12 - a, 0], F) → E'
  49. Segment(D, D') → h_1
  50. Segment(E, E') → j_1