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Dilation Exploration by Ben Graber

Dilation Exploration by Ben Graber
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2015-03-23 22:41
Coordinate GeometryTransformationGeometric ConstructionSlider Animation
This example demonstrates how shapes transform under dilation when centered at different points on the coordinate plane. It involves core concepts like dilation, scale factor, and geometric transformations. Constructed using commands like Point, Polygon, and Dilate, it is suitable for middle school and above students learning about properties of geometric transformations.

GeoGebra Commands & Parameters

  1. Point(xAxis) → E
  2. Polygon(A, C, D, B) → poly1, a, c, d, b
  3. Dilate(A, ScaleE, E) → A'
  4. Dilate(C, ScaleE, E) → C'
  5. Dilate(D, ScaleE, E) → D'
  6. Dilate(B, ScaleE, E) → B'
  7. Polygon(A', C', D', B') → poly1', a', c', d', b'
  8. Dilate(A, ScaleA, A) → A'_1
  9. Dilate(C, ScaleA, A) → C'_1
  10. Dilate(D, ScaleA, A) → D'_1
  11. Dilate(B, ScaleA, A) → B'_1
  12. Polygon(A'_1, C'_1, D'_1, B'_1) → poly1'_1, a'_1, c'_1, d'_1, b'_1
  13. Dilate(A, ScaleF, F) → A'_2
  14. Dilate(C, ScaleF, F) → C'_2
  15. Dilate(D, ScaleF, F) → D'_2
  16. Dilate(B, ScaleF, F) → B'_2
  17. Polygon(A'_2, C'_2, D'_2, B'_2) → poly1'_2, a'_2, c'_2, d'_2, b'_2
  18. Dilate(A, ScaleH, H) → A'_3
  19. Dilate(C, ScaleH, H) → C'_3
  20. Dilate(D, ScaleH, H) → D'_3
  21. Dilate(B, ScaleH, H) → B'_3
  22. Polygon(A'_3, C'_3, D'_3, B'_3) → poly1'_3, a'_3, c'_3, d'_3, b'_3

AI Drawing Prompt Reference

Draw a polygon in the coordinate plane, then dilate it multiple times using different scale factors centered at the x-axis point, one vertex of the polygon, and another arbitrary point, to show how the shape transforms under dilation with different centers.
The prompt above was compiled from the original drawing commands and is for reference only.