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Dilations of Line Segments

Dilations of Line Segments
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2018-01-22 03:59
FunctionTransformationGeometric Construction
This example demonstrates dilations of line segments. Key mathematical concepts include similarity transformations, line segments, and quadratic functions. Using GeoGebra commands such as Line, Dilate, Intersect, etc., the example constructs the dilation of line segments. Suitable for middle school and above students to learn about similarity transformations.

GeoGebra Commands & Parameters

  1. Line(B, C) → m
  2. Dilate(m, k, O) → m'
  3. Intersect(m, t) → O_1
  4. Line(O, C) → f
  5. Circle(C, 2) → g
  6. Intersect(m', f) → E
  7. Circle(E, 2) → h
  8. Intersect(g, m, 2) → F
  9. Intersect(g, f, 2) → G
  10. Intersect(h, m', 2) → H
  11. Intersect(h, f, 2) → I
  12. Intersect(g, m, 1) → J
  13. Intersect(g, f, 1) → K
  14. CircleSector(C, F, G) → q
  15. Angle(F, C, G) → α
  16. Angle(J, C, G) → β
  17. CircleSector(C, J, G) → c
  18. Intersect(h, m', 1) → N
  19. Dilate(C, 1 - i, E) → C'_3
  20. Vector(C, C'_3) → u
  21. Translate(q, u) → q'
  22. Translate(c, u) → c'
  23. Circle(O, 2) → e
  24. Segment(B, C) → preimage
  25. Dilate(B, k, O) → B'_2
  26. Dilate(C, k, O) → C'_1
  27. Segment(B'_2, C'_1) → image
  28. Dilate(B, k, O) → B'
  29. Dilate(C, k, O) → C'
  30. Point(m') → A
  31. Ray(C', A) → j
  32. Point(j) → D
  33. Point(m) → P
  34. Ray(C, P) → l
  35. Point(l) → Q
  36. Slope(image) → m_1
  37. Slope(image) → m_2
  38. Slope(preimage) → m_3
  39. Slope(preimage) → m_4