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Exploring Dilations

Exploring Dilations
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2020-01-17 03:46
Coordinate GeometryTransformationGeometric Construction
This example demonstrates changes in dimension and angle during geometric dilations. It involves core concepts like scale factor, length ratios, angle invariance, and area scaling. GeoGebra commands and objects used include Intersect, Polygon, Distance, Angle, Dilate, and Line. Suitable for high school students studying geometric transformations, coordinate geometry, and conic sections.

GeoGebra Commands & Parameters

  1. Intersect(0, 0) → A
  2. Polygon(C, D, E) → t1, e, c, d
  3. Distance(C, D) → distanceCD
  4. Distance(C, E) → distanceCE
  5. Distance(D, E) → distanceDE
  6. Angle(D, C, E) → α
  7. Angle(E, D, C) → β
  8. Angle(C, E, D) → γ
  9. Dilate(C, a, B) → C'
  10. Dilate(D, a, B) → D'
  11. Dilate(E, a, B) → E'
  12. Polygon(C', D', E') → t1', e', c', d'
  13. Line(C', B) → f
  14. Line(D', B) → g
  15. Line(E', B) → h
  16. Angle(D', C', E') → δ
  17. Angle(E', D', C') → ε
  18. Angle(C', E', D') → ζ
  19. Distance(D', C') → distanceD'C'
  20. Distance(C', D') → distanceC'D'
  21. Distance(C', E') → distanceC'E'
  22. Distance(D', E') → distanceD'E'