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Dilating a Line Segment by amit.quackenbush

Dilating a Line Segment by amit.quackenbush
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2017-03-24 20:32
VectorSolid GeometryTransformationGeometric Construction
This example demonstrates the dilation of a line segment in three-dimensional space. Key math concepts include line segments, transformations, vectors, and 3D geometry. Construction highlights involve GeoGebra commands such as Line, Dilate, Intersect, Circle, CircleSector, Angle, Vector, Translate, Segment, Point, and Ray. Suitable for high school and above students studying 3D transformations and vector mathematics.

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