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Animation 173: Circle Transformation

Animation 173: Circle Transformation
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2017-01-22 04:25
CircleVectorTransformation
This example demonstrates the transformation process of a circle, involving concepts such as circle, vector, and transformation. Using GeoGebra commands like Midpoint, Dilate, Rotate, and Intersect, it shows the translation, enlargement, and rotation of a circle. Suitable for high school mathematics education, especially for coordinate geometry and transformation-related courses.

GeoGebra Commands & Parameters

  1. Midpoint(A, B) → C
  2. Dilate(A, If[0 < a ≤ 1, 1 - a, 0], C) → A'
  3. Dilate(C, If[1 < a ≤ 2, 2 - a, 0], B) → C'
  4. Segment(A, A') → j
  5. Segment(C, C') → k
  6. Rotate(A, If[2 < a ≤ 3, ((a - 2) * π), π], C) → A'_1
  7. Rotate(A', If[2 < a ≤ 3, ((a - 2) * π), π], C) → A''
  8. Segment(A'_1, A'') → j'
  9. Intersect(i, l) → D
  10. Intersect(f, i) → E
  11. Dilate(E, If[6 < a ≤ 7, 7 - a, 0], D) → E'
  12. Segment(E, E') → m
  13. Dilate(D, If[7 < a ≤ 8, 8 - a, 0], B) → D'
  14. Segment(D, D') → n
  15. Rotate(E, If[8 < a ≤ 9, ((a - 8) * π), π], D) → E'_1
  16. Rotate(E', If[8 < a ≤ 9, ((a - 8) * π), π], D) → E''
  17. Segment(E'_1, E'') → m'
  18. Dilate(B, If[10 < a ≤ 11, 11 - a, 0], D) → B'
  19. Dilate(E, If[10 < a ≤ 11, 11 - a, 0], D) → E'_2
  20. Vector(E, E'_2) → u
  21. Vector(B, B') → v
  22. Intersect(f, p) → F
  23. Intersect(g, p) → G
  24. Dilate(E, If[12 < a ≤ 13, 13 - a, 0], F) → E'_3
  25. Dilate(B, If[12 < a ≤ 13, 13 - a, 0], G) → B'_1
  26. Vector(E, E'_3) → w
  27. Vector(B, B'_1) → b
  28. Translate(D, w) → D'_1
  29. Vector(E'_3, D'_1) → c
  30. Vector(B'_1, D'_1) → d
  31. Dilate(A, If[6 < a ≤ 7, 7 - a, 0], F) → A'_2
  32. Segment(A, A'_2) → q
  33. Dilate(F, If[7 < a ≤ 8, 8 - a, 0], E) → F'
  34. Segment(F, F') → r
  35. Rotate(A, If[8 < a ≤ 9, ((a - 8) * π), π], F) → A'_3
  36. Rotate(A'_2, If[8 < a ≤ 9, ((a - 8) * π), π], F) → H
  37. Segment(A'_3, H) → q'
  38. Dilate(A, If[10 < a ≤ 11, 11 - a, 0], F) → A'_4
  39. Dilate(E, If[10 < a ≤ 11, 11 - a, 0], F) → E'_4
  40. Vector(A, A'_4) → s
  41. Vector(E, E'_4) → t
  42. Dilate(F, If[12 < a ≤ 13, 13 - a, 0], MIDPOINT) → I
  43. Vector(F, I) → u_1
  44. Translate(A, u_1) → A'_5
  45. Vector(A'_5, I) → v_1
  46. Translate(E, u_1) → E'_5
  47. Vector(E'_5, I) → w_1
  48. Translate(F, u_1) → F'_1