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Dilating a Line by John Williams

Dilating a Line by John Williams
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2016-11-29 12:08
VectorTransformationGeometric Construction
In collections Dilation Introduction
This example demonstrates how to use dilation (scaling) to study a line that does not pass through the center of dilation. Key mathematical concepts include similarity transformation, lines, and the center of dilation. Commands used include Line, Dilate, Intersect, etc. Suitable for high school geometry lessons.

GeoGebra Commands & Parameters

  1. Line(B, C) → m
  2. Dilate(m, k, A) → m'
  3. Intersect(m, t) → O
  4. Line(A, 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'
  20. Vector(C, C') → u
  21. Translate(q, u) → q'
  22. Translate(c, u) → c'
  23. Circle(A, 2) → e

AI Drawing Prompt Reference

Draw a line and its dilation image with a center off the line. Intersect a circle with the line and the image to find two points, then draw circles centered at these points. Connect the center of dilation to the intersection points of the circle with the line and image. Highlight key angles, sectors, and translate sectors using a vector to show the dilation effect.
The prompt above was compiled from the original drawing commands and is for reference only.