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Exploring Dilations on the Coordinate Plane by Kim Kembitzky

Exploring Dilations on the Coordinate Plane by Kim Kembitzky
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2017-04-01 06:52
Coordinate GeometryTransformationGeometric Construction
This example demonstrates the process of performing dilation on the coordinate plane. The core math concepts involved include dilation, incircle or inscribed circle, angles, real numbers, orthocenter, and tangent line or tangent. Constructed using GeoGebra commands: Polygon, Dilate, Segment, Line; objects: A, B, C, poly1, c, a, b, Center, ScaleFactor, A', B', C', poly1', c', a', b', f, g, h, i, j, k, d, e, center, D, E, l, F, m, n, p, q. Suitable for high school mathematics geometry section, for understanding and practicing dilation transformations and their related properties.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Dilate(A, ScaleFactor, Center) → A'
  3. Dilate(B, ScaleFactor, Center) → B'
  4. Dilate(C, ScaleFactor, Center) → C'
  5. Polygon(A', B', C') → poly1', c', a', b'
  6. Segment(Center, C) → f
  7. Segment(C, C') → g
  8. Segment(Center, A) → h
  9. Segment(A, A') → i
  10. Segment(Center, B) → j
  11. Segment(Center, B') → k
  12. Line(D, E) → l
  13. Line(F, E) → m
  14. Line(Center, l) → n
  15. Line(Center, m) → p
  16. Line(Center, p) → q

AI Drawing Prompt Reference

Draw a triangle ABC, then dilate it by a scale factor of 2 with a center point to get triangle A'B'C'. Next, draw the lines connecting the midpoints of corresponding sides of triangles ABC and A'B'C', and the lines connecting each side of triangle ABC to its corresponding side.
The prompt above was compiled from the original drawing commands and is for reference only.