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Properties of Dilations

Properties of Dilations
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2019-04-05 02:51
PolygonTransformationGeometric ConstructionSlider Animation
①This interactive GeoGebra example demonstrates the properties of dilations by showing how a polygon and its image under a dilation maintain shape while changing size, with corresponding sides parallel or collinear. ②Core mathematical concepts include the center of dilation, scale factor, similarity, collinearity of corresponding points, and proportional relationships between corresponding segments; it also incorporates rotation and quadratic functions as auxiliary elements for comparison. ③Construction details: using GeoGebra commands Polygon, Segment, Textfield, and Dilate, the example builds triangle poly1 and its dilated image poly1', with a slider k controlling the scale factor and an input box for parameter entry; objects include original points A, B, C, center O, scaled points A', B', C', corresponding sides a', b', c', and auxiliary segments g, h, i, j, l, m for labeling properties. ④Suitable for middle-to-high school students learning geometric transformations, particularly to explore the definition and properties of dilations, their relation to similarity and congruence, and as a classroom demonstration or self-study tool.

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 its dilated image to demonstrate the properties of dilation. Use a slider to control the scale factor, connect the center of dilation to the corresponding vertices before and after dilation, and draw auxiliary segments from the center to each vertex. Label the corresponding sides and vertices, and display the scale factor, emphasizing that corresponding sides are parallel and lengths are proportional, and corresponding vertices are collinear, while showing the relation between dilation and similarity.
The prompt above was compiled from the original drawing commands and is for reference only.