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Similarity Transformation

Similarity Transformation
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2020-10-31 07:46
FunctionCoordinate GeometryTransformation
This example demonstrates the concept of similarity transformation, involving key mathematical concepts such as similarity ratio and median value. Using GeoGebra commands like Polygon, Intersect, and Dilate, the example constructs similar transformations. Suitable for students at the junior high school level and above.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → q1, a, b, c, d
  2. Intersect(xAxis, yAxis) → E
  3. Angle(B, A, D) → α
  4. Angle(A, B, C) → β
  5. Angle(B, C, D) → γ
  6. Angle(C, D, A) → δ
  7. Dilate(A, k, E) → A'
  8. Dilate(B, k, E) → B'
  9. Dilate(C, k, E) → C'
  10. Dilate(D, k, E) → D'
  11. Polygon(A', B', C', D') → q1', a', b', c', d'
  12. Angle(B', A', D') → ε
  13. Angle(A', B', C') → ζ
  14. Angle(B', C', D') → η
  15. Angle(A', D', C') → θ
  16. Line(D, D') → f
  17. Line(A, A') → g
  18. Line(C, C') → h
  19. Line(B, B') → i
  20. Distance(E, D) → distanceED
  21. Distance(E, D') → distanceED'
  22. Distance(E, A) → distanceEA
  23. Distance(E, A') → distanceEA'
  24. Distance(E, C) → distanceEC
  25. Distance(E, C') → distanceEC'
  26. Distance(E, B) → distanceEB
  27. Distance(E, B') → distanceEB'
  28. Distance(E, B') → e

AI Drawing Prompt Reference

Draw a quadrilateral and mark its four interior angles. Locate the intersection point of its diagonals as the center. Apply a dilation with a given scale factor about this center to create a second quadrilateral. Label the corresponding angles of the dilated quadrilateral. Connect each original vertex to its dilated counterpart with straight lines, all passing through the center. Measure and display distances from the center to each original and dilated vertex to illustrate the similarity ratio. The figure should clearly show the similarity transformation and proportional relationships.
The prompt above was compiled from the original drawing commands and is for reference only.