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Animation 60: Geometric Transformations and Function Demonstrations

Animation 60: Geometric Transformations and Function Demonstrations
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2016-06-21 18:49
FunctionTrigonometryTransformationGeometric Construction
In collections Congruence (CO) Cluster Congruence (Vol 2) CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Parallel Lines and Planes
This example demonstrates geometric transformations such as rotation, dilation, and intersection of points, lines, and circles through animation, combined with dynamic changes in function and trigonometric function graphs. Core mathematical concepts include angles, straight lines, matrix transformations, function graphs, cones, trigonometric functions, and the unit circle. Construction highlights the use of commands like Point, Rotate, Angle, Line, Circle, Intersect, CircleSector, Dilate, Vector, Midpoint, Segment, Ray, and CircleArc in GeoGebra. Suitable for high school and above students to understand the dynamic relationship between geometric transformations and function graphs, as well as practical applications.

GeoGebra Commands & Parameters

  1. Point(a) → B
  2. Rotate(B, α, A) → B'
  3. Angle(B, A, B') → β
  4. Line(A, B') → b
  5. Circle(A, 1) → e
  6. Intersect(b, d) → C
  7. Circle(C, 1) → f
  8. Intersect(e, a) → D, E
  9. Intersect(e, b) → F, G
  10. Intersect(f, b) → H, I
  11. Intersect(f, d) → J, K
  12. CircleSector(C, J, H) → k
  13. CircleSector(C, H, K) → p
  14. CircleSector(A, F, E) → t
  15. Dilate(A, If[0 < i < 1, 1 - i], C) → A'
  16. Vector(A, A') → u
  17. Vector(A, C) → v
  18. Midpoint(C, A) → L
  19. Rotate(A, (((-i) * 180))°, L) → A'_1
  20. Segment(L, A'_1) → g
  21. Segment(C, L) → n
  22. Segment(L, A) → s
  23. Point(b) → M
  24. Point(b) → N
  25. Ray(C, M) → a_1
  26. Ray(A, N) → b_1
  27. Rotate(E, (((-i) * 180))°, L) → E'
  28. Ray(A'_1, E') → d_1
  29. Circle(A'_1, Distance[L, A'_1]) → e_1
  30. Intersect(e_1, d_1, 1) → O
  31. Rotate(A, ((i * 180))°, L) → A'_2
  32. Rotate(D, ((i * 180))°, L) → D'
  33. Circle(A'_2, L) → k_1
  34. Ray(A'_2, D') → i_1
  35. Intersect(k_1, i_1) → P,
  36. Segment(A'_2, P) → j_1
  37. Intersect(e, b, 1) → Q
  38. Intersect(f, n, 1) → R
  39. CircleSector(A, Q, E) → c_1
  40. Rotate(Q, (((-i) * 180))°, L) → Q'
  41. Circle(A, g) → g_1
  42. Intersect(g_1, b_1, 1) → S
  43. Intersect(g_1, a, 2) → T
  44. Segment(A, S) → h_1
  45. Rotate(A, (((-i) * 180))°, L) → A'_3
  46. Rotate(S, (((-i) * 180))°, L) → S'
  47. Segment(A'_3, S') → l_1
  48. Segment(A, T) → m_1
  49. Rotate(A, (((-i) * 180))°, L) → A'_4
  50. Rotate(T, (((-i) * 180))°, L) → T'
  51. Segment(A'_4, T') → n_1
  52. CircleArc(A, Q, E) → p_1
  53. Intersect(e_1, a, 1) → U
  54. Segment(A, U) → q_1
  55. Intersect(a, q_1) → V
  56. Intersect(a, q_1) → W
  57. Intersect(e, a, 1) → Z
  58. CircleSector(A, Z, Q) → r
  59. Rotate(A, ((i * 180))°, L) → A'_5
  60. Rotate(r, ((i * 180))°, L) → r'
  61. Rotate(A, ((i * 180))°, L) → A'_6
  62. Rotate(S, ((i * 180))°, L) → S'_1
  63. Segment(A'_6, S'_1) → h
  64. Segment(L, A'_5) → r_1
  65. CircleArc(A, Z, Q) → f_1
  66. Rotate(c_1, If[0 < i ≤ 1, ((-i) * π), (-π)], L) → q

AI Drawing Prompt Reference

Create a dynamic illustration showing geometric transformations like rotation and dilation, and the intersection of points, lines, and circles. Include animated changes in function and trigonometric graphs, highlighting angles, straight lines, matrix transformations, and function graphs. Suitable for high school students to understand the dynamic relationship between geometric transformations and function graphs.
The prompt above was compiled from the original drawing commands and is for reference only.