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Properties of Dilations by Raluca Radu

Properties of Dilations by Raluca Radu
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2018-03-05 12:49
Coordinate GeometryTransformationGeometric Construction
This example demonstrates the properties of dilations in similarity transformations. Key mathematical concepts include similarity transformations and similar figures. Using GeoGebra commands such as Dilate, Polygon, etc., the example dynamically shows the scaling effects on points, segments, and polygons. Suitable for students at the middle school level and above to learn about the concept and applications of similarity transformations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Segment(A, B) → d
  3. Segment(B, C) → e
  4. Segment(C, A) → f
  5. Textfield(k) → InputBox1
  6. Dilate(A, k, O) → A'
  7. Dilate(B, k, O) → B'
  8. Dilate(C, k, O) → C'
  9. Polygon(A', B', C') → poly1', c', a', b'
  10. Dilate(A, k, O) → A'_1
  11. Dilate(B, k, O) → B'_1
  12. Segment(A'_1, B'_1) → d'
  13. Dilate(B, k, O) → B'_2
  14. Dilate(C, k, O) → C'_1
  15. Segment(B'_2, C'_1) → e'
  16. Dilate(C, k, O) → C'_2
  17. Dilate(A, k, O) → A'_2
  18. Segment(C'_2, A'_2) → f'
  19. Segment(O, A') → g
  20. Segment(O, A) → h
  21. Segment(O, B) → i
  22. Segment(O, B') → j
  23. Segment(O, C') → l
  24. Segment(O, C) → m

AI Drawing Prompt Reference

Draw a triangle and three points, connect them to form a triangle. Then, dilate the triangle and the three points from a center point by the same scale to get new triangle and points, and connect them. Finally, connect the center point to the vertices of the dilated and original triangles to show the scaling effects of similarity transformations.
The prompt above was compiled from the original drawing commands and is for reference only.