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Introduction to Dilations

Introduction to Dilations
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2019-05-04 00:21
TrianglePolygonTransformationGeometric ConstructionSlider Animation
① This interactive GeoGebra applet demonstrates the dilation (scaling) of a triangle about a center O with a scale factor k, showing the original figure and its image side by side. ② The core mathematical concept is dilation, a similarity transformation where corresponding points lie on lines through the center and distances are multiplied by the scale factor; it also involves polygons, isosceles triangles, and geometric transformations. ③ Construction highlights: the applet uses the Polygon command to create triangle ABC, Segment for edges, Textfield and InputBox1 for entering the scale factor k, and the Dilate command to generate the image triangle A'B'C' and its sides, with connecting segments (d, e, f) to visualize the correspondence. ④ This is suitable for middle or high school geometry lessons on similarity transformations, dilation properties, and can be used as a classroom demonstration or student exploration worksheet.

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 triangle ABC and dilate it about point O using a slider to control the scale factor k, resulting in triangle A'B'C'. Display both triangles side by side, connect corresponding vertices A to A', B to B', C to C', and draw lines from O to A', B', C' and from O to A, B, C to visualize the dilation and similarity transformation.
The prompt above was compiled from the original drawing commands and is for reference only.