MathPlotAI Logo MathPlotAI

Dilating a Segment

Dilating a Segment
Loading the math board and drawing, please wait…
2016-11-29 12:22
VectorTransformationGeometric Construction
This example illustrates that under a dilation with scale factor k, the image of a segment remains a segment, is parallel to the original, and its length is k times the original. Key math concepts include similarity transformation, scale factor, parallel lines, and segment length ratio. GeoGebra commands and objects used are Line, Dilate, Intersect, Circle, CircleSector, Angle, Vector, Translate, Segment, Point, and Ray. Suitable for high school students and teachers learning about similarity transformations and geometric constructions.

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 diagram illustrating a similarity transformation with scale factor k. Start by drawing a line segment BC, then dilate it from point O by factor k to get BC'. Show that the new segment is parallel to the original and its length is k times the original. Use circles and intersections to mark key points E, F, G, H, I, J, K, and draw sectors and vectors to complete the illustration.
The prompt above was compiled from the original drawing commands and is for reference only.