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Dilation of the Triangle

Dilation of the Triangle
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2016-04-11 16:11
TriangleTransformationGeometric Construction
This example demonstrates the dilation transformation of a triangle. The core mathematical concepts involved include dilation, equilateral triangles, probability, piecewise functions, and limits. The construction utilizes GeoGebra commands such as Polygon, Ray, Distance, Circle, Intersect; objects include N, A_1, B_1, C_1, poly1, c_1, a_1, b_1, D, e, d, f, distanceDA, a, distanceDC, distanceDB, b, g, E, h, F, k, G, poly2, f_1, e_1, g_1, H, B, C, poly3, j, h_1, A. It is suitable for high school students learning geometric transformations and probability & statistics.

GeoGebra Commands & Parameters

  1. Polygon(A_1, B_1, C_1) → poly1, c_1, a_1, b_1
  2. Ray(D, B_1) → e
  3. Ray(D, A_1) → d
  4. Ray(D, C_1) → f
  5. Distance(D, A_1) → distanceDA
  6. Distance(D, C_1) → distanceDC
  7. Distance(D, B_1) → distanceDB
  8. Circle(D, (N * Distance[D, A_1])) → g
  9. Intersect(g, d, 1) → E
  10. Circle(D, (N * Distance[D, C_1])) → h
  11. Intersect(h, f, 1) → F
  12. Circle(D, (N * Distance[D, B_1])) → k
  13. Intersect(k, e, 1) → G
  14. Polygon(E, G, F) → poly2, f_1, e_1, g_1
  15. Intersect(b_1, f) → H
  16. Intersect(c_1, e) → B
  17. Intersect(c_1, b_1) → C
  18. Polygon(H, B, C) → poly3, j, h_1, A