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Dilations Exploration by Keith Hatfield

Dilations Exploration by Keith Hatfield
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2015-12-19 01:43
PolygonTransformationGeometric Construction
This example demonstrates the transformation of shapes through similarity transformations (scaling) and its underlying principles. Key math concepts include similarity transformation, proportionality, distance measurement, and polygon construction. GeoGebra commands/objects used are Intersect, Polygon, Ray, Distance, and Dilate. Suitable for middle school students and above to learn geometric transformations and proportional relationships, as well as high school coordinate geometry instruction.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Polygon(B, C, D) → poly1, d, b, c
  3. Ray(A, B) → a
  4. Ray(A, C) → e
  5. Ray(A, D) → f
  6. Distance(A, B) → distanceAB
  7. Distance(B, C) → distanceBC
  8. Distance(B, D) → distanceBD
  9. Dilate(B, Scale, A) → B'
  10. Dilate(C, Scale, A) → C'
  11. Dilate(D, Scale, A) → D'
  12. Polygon(B', D', C') → poly2, c', b', d'
  13. Distance(B, A) → distanceBA
  14. Distance(B, A) → g
  15. Distance(A, B) → h
  16. Distance(A, B) → i
  17. Distance(A, B') → distanceAB'
  18. Distance(A, D') → distanceAD'
  19. Distance(A, C') → distanceAC'
  20. Distance(A, D') → j
  21. Distance(A, B) → k
  22. Distance(A, C) → distanceAC
  23. Distance(A, D) → distanceAD
  24. Distance(B, D) → l
  25. Distance(C, D) → distanceCD
  26. Distance(B', D') → distanceB'D'
  27. Distance(B', C') → distanceB'C'
  28. Distance(D', C') → distanceD'C'
  29. Distance(B, C) → m
  30. Distance(D, C) → distanceDC

AI Drawing Prompt Reference

Draw a rectangle ABCD, then dilate it by a scale factor of 2 centered at point A to get a new rectangle A'B'C'D'. First, draw the intersection point A of the x-axis and y-axis, then draw the three vertices B, C, D of the rectangle ABCD, next draw three rays from A to B, C, D, measure the lengths of AB, BC, CD, DA, then dilate B, C, D by a scale factor of 2 to get B', C', D', finally draw the new rectangle A'B'C'D'.
The prompt above was compiled from the original drawing commands and is for reference only.