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Dilating a Segment by Aaron Dankman

Dilating a Segment by Aaron Dankman
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2016-12-06 05:35
VectorCoordinate GeometryTransformationGeometric Construction
In collections Dilation Introduction
This example demonstrates the properties of a segment's image under a dilation with scale factor k, showing that the image is parallel to the original and k times its length. It involves core concepts like similarity transformation, scale factor, parallelism, and segment length change. Constructed using GeoGebra commands: Line, Dilate, Intersect, Circle, CircleSector, Angle, Vector, Translate, Segment, Point, Ray. Suitable for high school students learning about similarity transformations and their applications.

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

AI Drawing Prompt Reference

Draw a segment BC and a point O as the center of dilation. Dilate segment BC by scale factor k about O to obtain a parallel image segment with length k times the original. Construct two lines through O intersecting both segments at corresponding points. Draw equal-radius circles centered at these intersection points, marking their intersections with the lines. Use circular sectors and angle markers to show corresponding angles. Translate the sectors by a vector to illustrate the preservation of shape and angle under dilation. Finally, draw rays from O through points on the image segment extending to the original segment, completing the dilation relationship diagram.
The prompt above was compiled from the original drawing commands and is for reference only.