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Dilation and Ratio of Distances

Dilation and Ratio of Distances
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2020-02-02 04:18
TriangleTransformationGeometric Construction
This example demonstrates the similarity and ratio of side lengths under similarity transformations without complex distance formula calculations. Using GeoGebra commands like Polygon, Segment, Textfield, Dilate, and Distance, it constructs and observes triangle OAB and its dilated triangle O'A'B'. Point O is the center of dilation, k is the scale factor, and d represents the ratio of distances between corresponding sides. Suitable for high school geometry teaching and exploration of similarity triangles, transformations, and ratios.

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
  25. Distance(B, A) → distanceBA
  26. Distance(B, C) → distanceBC
  27. Distance(C, A) → distanceCA
  28. Distance(B', C') → distanceB'C'
  29. Distance(C', A') → distanceC'A'
  30. Distance(A', B') → distanceA'B'

AI Drawing Prompt Reference

Draw triangle OAB and then dilate it from point O with scale factor k to get triangle O'A'B'. Observe the similarity and the ratio of corresponding side lengths. Label the distances from O to each vertex and measure the lengths of the sides before and after dilation to verify the scale factor.
The prompt above was compiled from the original drawing commands and is for reference only.