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Dilation Demonstration

Dilation Demonstration
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2016-10-20 20:02
PolygonCoordinate GeometryTransformationGeometric Construction
This example demonstrates the effect of similarity transformations (scaling) on shapes, particularly polygons and cones. Core math concepts include similarity transformation, proportion, perimeter, and curve sketching. Construction highlights using GeoGebra commands: Polygon, Line, Intersect, Dilate, Point. Suitable for high school geometry students to understand and apply properties of similarity transformations and calculate perimeter changes after transformation.

GeoGebra Commands & Parameters

  1. Polygon(C, A, B) → poly1, c, a, b
  2. Line(W, xAxis) → f_2
  3. Line(W, yAxis) → g_2
  4. Line(C, f_2) → h
  5. Line(C, g_2) → i
  6. Intersect(f_2, i) → E
  7. Intersect(g_2, h) → F
  8. Polygon(W, E, C, F) → poly2, d_6, e, a_1, f_1
  9. Line(B, f_2) → j
  10. Line(B, g_2) → k
  11. Intersect(f_2, k) → G
  12. Intersect(g_2, j) → H
  13. Polygon(W, G, B, H) → poly3, d_1, g_1, c_1, h_1
  14. Line(A, g_2) → l
  15. Line(A, d_6) → m
  16. Intersect(f_2, l) → I
  17. Intersect(g_2, m) → J
  18. Polygon(W, I, A, J) → poly4, d_2, i_1, b_1, j_1
  19. Dilate(C, n, W) → C'
  20. Dilate(A, n, W) → A'
  21. Dilate(B, n, W) → B'
  22. Polygon(C', A', B') → poly1', c', a', b'
  23. Line(B', g_2) → p
  24. Line(B', f_2) → q
  25. Line(A', f_2) → r_2
  26. Line(A', g_2) → s
  27. Line(C', f_2) → t_1
  28. Line(C', s) → k_1
  29. Point(p) → K
  30. Intersect(g_2, q) → L
  31. Intersect(g_2, r_2) → M
  32. Intersect(f_2, s) → N
  33. Polygon(W, M, A', N) → poly6, d_4, m_1, b'_1, n_1
  34. Intersect(f_2, k_1) → O
  35. Intersect(g_2, t_1) → P
  36. Polygon(W, O, C', P) → hT, d_5, o, a'_1, p_1
  37. Intersect(f_2, p) → Q
  38. Intersect(g_2, q) → R
  39. Polygon(W, Q, B', R) → poly5, d_3, q_1, c'_1, r_1