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Rotation Transformation Exploration by cary.hoste

Rotation Transformation Exploration by cary.hoste
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2015-11-30 06:17
PolygonTransformationGeometric Construction
This example demonstrates the effects and properties of rotation transformations on shapes. The core mathematical concepts involved include rotation, geometric transformation, and polygon construction. The construction highlights the use of GeoGebra commands such as Point, Intersect, Polygon, Rotate, Line, and Mirror to precisely construct and manipulate shapes, observing changes during rotation. It is suitable for high school students studying geometric transformations and spatial geometry, helping them understand the mathematical principles and practical applications of rotation transformations.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Intersect(xAxis, yAxis) → C_1
  3. Polygon(A, B_1, C_1) → poly1, c, a, b
  4. Rotate(A, 180*°, C_1) → E_2
  5. Rotate(B_1, 180*°, C_1) → B'
  6. Rotate(C_1, 180*°, C_1) → C'
  7. Polygon(E_2, B', C') → poly1', c', a', b'
  8. Line(A, C_1) → e_2
  9. Mirror(A, b) → A'
  10. Mirror(B_1, b) → B'_1
  11. Mirror(C_1, b) → C'_1
  12. Polygon(A', B'_1, C'_1) → poly1'_1, c'_1, a'_1, b'_1
  13. Mirror(A', xAxis) → D_1
  14. Mirror(B'_1, xAxis) → E_1
  15. Mirror(C'_1, xAxis) → F_1
  16. Polygon(D_1, E_1, F_1) → poly2, f, d_1, e_1
  17. Point(xAxis) → G_1
  18. Line(C_1, G_1) → g
  19. Mirror(A', g) → H_1
  20. Mirror(B'_1, g) → I
  21. Mirror(C'_1, g) → J
  22. Polygon(H_1, I, J) → poly3, j, h, i
  23. Mirror(A', g) → E
  24. Mirror(B'_1, g) → L
  25. Mirror(C'_1, g) → M
  26. Polygon(E, L, M) → poly4, m, k, l
  27. Mirror(E_2, b') → A''
  28. Mirror(B', b') → B''
  29. Mirror(C', b') → C''
  30. Polygon(A'', B'', C'') → poly1'', c'', a'', b''
  31. Point(g) → C
  32. Polygon(C_1, B'_1, C) → poly5, n, c_1, b'_2
  33. Mirror(C_1, b'_2) → C'_2
  34. Mirror(B'_1, b'_2) → O_1
  35. Mirror(C, b'_2) → N'
  36. Polygon(C'_2, O_1, N') → poly5', n', c'_2, o
  37. Mirror(C_1, b) → C'_3
  38. Mirror(B'_1, b) → P
  39. Mirror(C, b) → N'_1
  40. Polygon(C'_3, P, N'_1) → poly5'_1, n'_1, c'_3, p
  41. Mirror(C'_2, b) → O
  42. Mirror(O_1, b) → O'
  43. Mirror(N', b) → G
  44. Polygon(O, O', G) → poly5'', n'', q, o'
  45. Intersect(n'_1, c'_3) → H
  46. Intersect(c'_1, a'_1) → B
  47. Intersect(c', a') → D
  48. Intersect(c'', a'') → F
  49. Polygon(G, H, A, B, C, D, E, F) → poly6, g_1, k_1, a_1, n_1, c_2, q_1, e, r