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Dilations Part 3: What Do You Notice?

Dilations Part 3: What Do You Notice?
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2023-03-10 03:44
TriangleTransformationGeometric Construction
In collections Exploring Dilations
This example demonstrates the effects of dilation on geometric figures. Key mathematical concepts include similar triangles, similarity transformations, and geometric construction. The construction involves GeoGebra commands such as Segment, Dilate, OrthogonalLine, and others. Suitable for middle or high school mathematics to understand the principles and applications of dilation.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Dilate(A, k, C) → A'
  3. Dilate(B, k, C) → B'
  4. Segment(A', B') → f'
  5. Segment(C, A) → g
  6. Segment(C, B) → i
  7. Segment(A, A') → h
  8. Segment(B, B') → j
  9. OrthogonalLine(C, g) → l
  10. OrthogonalLine(A', h) → m
  11. Circle(C, 1.5) → c
  12. Intersect(c, l, 2) → D
  13. OrthogonalLine(D, l) → n
  14. OrthogonalLine(C, j) → p
  15. OrthogonalLine(B', j) → q
  16. Intersect(c, p, 1) → E
  17. OrthogonalLine(E, p) → r
  18. Intersect(q, r) → F
  19. Intersect(m, n) → G
  20. Point(m) → H
  21. OrthogonalLine(H, m) → s
  22. Intersect(l, s) → I
  23. Segment(H, I) → t
  24. Line(C, E) → a
  25. Point(q) → J
  26. OrthogonalLine(J, q) → b
  27. Intersect(a, b) → K
  28. Segment(J, K) → d

AI Drawing Prompt Reference

Draw a triangle ABC, then perform a similarity transformation centered at point C to get triangle A'B'. Construct the perpendicular bisectors g and i of AC and BC, and the perpendicular bisectors h and j of AA' and BB'. Find the intersection of a circle centered at C with radius 1.5 and the perpendicular to g, then construct the perpendicular to h and find its intersection with the circle. Continue this process to create a complex, similar figure to the original triangle.
The prompt above was compiled from the original drawing commands and is for reference only.