MathPlotAI Logo MathPlotAI

Dilation of Triangles

Dilation of Triangles
Loading the math board and drawing, please wait…
2015-02-17 15:31
TriangleTransformationGeometric Construction
In collections Transformations Stations
This example demonstrates the concept of dilation using triangles. It shows how to change the size of a triangle while keeping its shape unchanged by adjusting the scale factor. Commands used include Polygon, Dilate, Sequence, Segment, and are suitable for students in middle school and above learning geometric transformations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, AB, BC, CA
  2. Dilate(A, n / d, Origin) → A'
  3. Dilate(B, n / d, Origin) → B'
  4. Dilate(C, n / d, Origin) → C'
  5. Polygon(A', B', C') → poly2, A'B', B'C', C'A'
  6. Sequence(Dilate[A, i / d, C], i, 1, d - 1) → list1
  7. Sequence(Dilate[C, i / d, B], i, 1, d - 1) → list2
  8. Sequence(Dilate[B, i / d, A], i, 1, d - 1) → list3
  9. Sequence(Dilate[A', i / n, C'], i, 1, n - 1) → list4
  10. Sequence(Dilate[C', i / n, B'], i, 1, n - 1) → list5
  11. Sequence(Dilate[B', i / n, A'], i, 1, n - 1) → list6
  12. Sequence(Segment[Element[list1, i], Element[list2, d - i]], i, 1, d - 1) → list7
  13. Sequence(Segment[Element[list1, i], Element[list3, d - i]], i, 1, d - 1) → list8
  14. Sequence(Segment[Element[list3, i], Element[list2, d - i]], i, 1, d - 1) → list9
  15. Sequence(Segment[Element[list4, i], Element[list5, n - i]], i, 1, n - 1) → list10
  16. Sequence(Segment[Element[list5, i], Element[list6, n - i]], i, 1, n - 1) → list11
  17. Sequence(Segment[Element[list6, i], Element[list4, n - i]], i, 1, n - 1) → list12
  18. Segment(Origin, C') → a
  19. Segment(Origin, B') → b
  20. Segment(Origin, A') → c
  21. Segment(Origin, C) → e
  22. Segment(Origin, A) → f
  23. Segment(Origin, B) → g
  24. Sequence(Dilate[C, i / d, Origin], i, 1, d - 1) → list13
  25. Sequence(Dilate[A, i / d, Origin], i, 1, d - 1) → list14
  26. Sequence(Dilate[B, i / d, Origin], i, 1, d - 1) → list15
  27. Sequence(Dilate[C', i / n, Origin], i, 1, n - 1) → list16
  28. Sequence(Dilate[B', i / n, Origin], i, 1, n - 1) → list17
  29. Sequence(Dilate[A', i / n, Origin], i, 1, n - 1) → list18
  30. Sequence(Polygon[Element[list16, i], Element[list17, i], Element[list18, i]], i, If[d < n, d + 1, 1], n - 1) → list20
  31. Sequence(Polygon[Element[list13, i], Element[list14, i], Element[list15, i]], i, If[n < d, n + 1, 1], d - 1) → list19

AI Drawing Prompt Reference

Draw two triangles, one in original size and one scaled-up but maintaining the same shape, to demonstrate resizing by scaling from a center point. Connect the vertices of the original triangle to the corresponding vertices of the scaled triangle with lines to show a gradual transition from original to scaled. Also, draw multiple line segments extending from the vertices of the original triangle through the center point, showing different scaling factors. Finally, use these segments to form intermediate-sized triangles, creating a continuous scaling transition effect.
The prompt above was compiled from the original drawing commands and is for reference only.