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Properties of Dilations by Jeff Hamilton

Properties of Dilations by Jeff Hamilton
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2017-01-19 03:32
VectorTransformationGeometric Construction
This example demonstrates the properties of dilations. It involves core concepts of similarity transformations, including scaling shapes. Using GeoGebra commands such as Dilate, Vector, Translate, and Rotate, the effect of similarity transformations can be constructed. Suitable for middle and high school students learning 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

AI Drawing Prompt Reference

Draw a triangle and dilate it about an external center point to form a second triangle. Connect the center to corresponding vertices and show the original and dilated sides. Place small circles at two vertices of the original triangle, intersecting adjacent sides to create two circular sectors, which translate during the dilation. Include an input box for the scale factor and two sliders to animate different stages of the transformation.
The prompt above was compiled from the original drawing commands and is for reference only.