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Dilation Properties Demo

Dilation Properties Demo
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2014-12-30 05:04
PolygonCoordinate GeometryTransformationGeometric Construction
This example demonstrates the properties of dilations given a center and scale factor through experimentation. It involves core math concepts like dilation, proportionality, polygon area changes, and segment length ratios. Constructed using GeoGebra commands such as Dilate, Polygon, Distance, Line, Area, Slope, Textfield, Segment, and Ray. Suitable for high school mathematics education to understand geometric properties and calculations of similarity transformations.

GeoGebra Commands & Parameters

  1. Dilate(A, s, Center) → A'
  2. Dilate(C, s, Center) → C'
  3. Dilate(B, s, Center) → B'
  4. Polygon(A, B, C) → poly1, c, a, b
  5. Polygon(A', B', C') → poly2, c', a', b'
  6. Distance(A, B) → distanceAB
  7. Distance(B, C) → distanceBC
  8. Distance(C, A) → distanceCA
  9. Distance(A', B') → distanceA'B'
  10. Distance(B', C') → distanceB'C'
  11. Distance(C', A') → distanceC'A'
  12. Line(A, B) → g
  13. Area(poly2) → Area2
  14. Area(poly1) → Area1
  15. Distance(Center, A') → distanceCenterA'
  16. Slope(g) → m_1
  17. Distance(Center, A) → distanceCenterA
  18. Distance(Center, C') → distanceCenterC'
  19. Distance(Center, C) → distanceCenterC
  20. Distance(Center, A') → o
  21. Distance(Center, A) → p
  22. Distance(Center, B') → distanceCenterB'
  23. Distance(Center, B) → distanceCenterB
  24. Slope(r) → m_3
  25. Dilate(r, s, Center) → r'
  26. Textfield(r) → inputBox2
  27. Slope(r') → m_4
  28. Segment((0, 0), (6, 0)) → d
  29. Dilate(d, s, Center) → d'
  30. Textfield(d) → inputBox1
  31. Line(A', B') → h
  32. Slope(h) → m_2
  33. Ray(Center, A) → k
  34. Ray(Center, C) → l
  35. Ray(Center, B) → m
  36. Ray(Center, A') → a_1
  37. Ray(Center, B') → b_1
  38. Ray(Center, C') → c_1

AI Drawing Prompt Reference

Draw a geometric diagram to demonstrate the properties of dilation. Include a center point, a polygon, and its dilated image. Calculate and display the areas of the original and dilated polygons, as well as the ratios of corresponding side lengths. Connect the vertices of the original and dilated polygons with line segments, and draw rays from the center point through each vertex. Label the scale factor and display the slopes of the corresponding rays.
The prompt above was compiled from the original drawing commands and is for reference only.