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Explore the Effect of Changing the Scale Factor for a Dilation

Explore the Effect of Changing the Scale Factor for a Dilation
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2016-10-05 21:35
TransformationGeometric Construction
This example demonstrates the effect of altering the scale factor on a dilation transformation. Key math concepts include dilation, similarity transformation, median value, arithmetic operations, cuboid, and translation. Construction highlights the use of GeoGebra commands and objects like Polygon, Segment, Textfield, Dilate, Circle, Intersect, CircleSector, Vector, Translate, Angle, and Rotate. Suitable for middle school and above students to understand the properties of geometric transformations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Segment(A, B) → d
  3. Segment(B, C) → e
  4. Segment(C, A) → f
  5. Textfield(k) → InputBox1
  6. Dilate(A, k, O) → A'
  7. Dilate(B, k, O) → B'
  8. Dilate(C, k, O) → C'
  9. Polygon(A', B', C') → poly1', c', a', b'
  10. Dilate(A, k, O) → A'_1
  11. Dilate(B, k, O) → B'_1
  12. Segment(A'_1, B'_1) → d'
  13. Dilate(B, k, O) → B'_2
  14. Dilate(C, k, O) → C'_1
  15. Segment(B'_2, C'_1) → e'
  16. Dilate(C, k, O) → C'_2
  17. Dilate(A, k, O) → A'_2
  18. Segment(C'_2, A'_2) → f'
  19. Segment(O, A') → g
  20. Segment(O, A) → h
  21. Segment(O, B) → i
  22. Segment(O, B') → j
  23. Segment(O, C') → l
  24. Segment(O, C) → m
  25. Circle(A, 1) → p
  26. Circle(B, 1) → s
  27. Intersect(p, f, 1) → D
  28. Intersect(p, d, 1) → E
  29. Intersect(s, d, 1) → F
  30. Intersect(s, e, 1) → G
  31. CircleSector(A, D, E) → t
  32. CircleSector(B, F, G) → c_1
  33. Dilate(A, If[0 < n ≤ 1, 1 - n, 0], A') → A'_3
  34. Dilate(B, If[1 < n ≤ 2, 2 - n, 0], B') → B'_3
  35. Vector(B, B'_3) → u
  36. Vector(A, A'_3) → v
  37. Translate(t, v) → t'
  38. Translate(c_1, u) → d_1
  39. Angle(D, A, E) → α
  40. CircleSector(A, E, D) → e_1
  41. CircleSector(B, G, F) → f_1
  42. Translate(e_1, v) → g_1
  43. Translate(f_1, u) → h_1
  44. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], A') → A'_4
  45. Vector(A, A'_4) → w
  46. Dilate(B, If[2 < o ≤ 3, 3 - o, 0], B') → B'_4
  47. Vector(B, B'_4) → q
  48. Translate(e_1, w) → r
  49. Rotate(r, If[1 < o ≤ 2, (((o - 1) * 180))°, 180°], A') → r'
  50. Translate(f_1, q) → k_1
  51. Rotate(k_1, If[3 < o ≤ 4, (((o - 3) * 180))°, 180°], B') → p_1
  52. Translate(t, w) → t'_1
  53. Rotate(t'_1, If[1 < o ≤ 2, (((o - 1) * 180))°, 180°], A') → q_1
  54. Translate(c_1, q) → r_1
  55. Rotate(r_1, If[3 < o ≤ 4, (((o - 3) * 180))°, 180°], B') → s_1