MathPlotAI Logo MathPlotAI

Properties of Dilations by Gabriel Davis

Properties of Dilations by Gabriel Davis
Loading the math board and drawing, please wait…
2015-12-15 21:13
TriangleTransformationGeometric Construction
This example demonstrates the effects of dilation (scaling) on a triangle, involving core concepts like center of dilation, scale factor, distance change, area change, and angle invariance. It uses GeoGebra commands such as Dilate, Polygon, Distance, Area, and Angle for construction, suitable for high school students learning geometric transformations.

GeoGebra Commands & Parameters

  1. Dilate(A, s, Center) → A'
  2. Dilate(C, s, Center) → C'
  3. Dilate(B, s, Center) → B'
  4. Polygon(A, B, C) → poly1, c, a, b
  5. Polygon(A', B', C') → poly2, c', a', b'
  6. Distance(A, B) → distanceAB
  7. Distance(B, C) → distanceBC
  8. Distance(C, A) → distanceCA
  9. Distance(A', B') → distanceA'B'
  10. Distance(B', C') → distanceB'C'
  11. Distance(C', A') → distanceC'A'
  12. Line(A, B) → g
  13. Area(poly2) → Area2
  14. Area(poly1) → Area1
  15. Distance(Center, A') → distanceCenterA'
  16. Slope(g) → m_1
  17. Distance(Center, A) → distanceCenterA
  18. Distance(Center, C') → distanceCenterC'
  19. Distance(Center, C) → distanceCenterC
  20. Distance(Center, A') → o
  21. Distance(Center, A) → p
  22. Distance(Center, B') → distanceCenterB'
  23. Distance(Center, B) → distanceCenterB
  24. Slope(r) → m_3
  25. Dilate(r, s, Center) → r'
  26. Slope(r') → m_4
  27. Line(A', B') → h
  28. Slope(h) → m_2
  29. Ray(Center, A) → k
  30. Ray(Center, C) → l
  31. Ray(Center, B) → m
  32. Ray(Center, A') → a_1
  33. Ray(Center, B') → b_1
  34. Ray(Center, C') → c_1
  35. Line(D, E) → e_1
  36. Dilate(e_1, s, Center) → f_1
  37. Segment(F, G) → g_1
  38. Dilate(F, s, Center) → F'
  39. Dilate(G, s, Center) → G'
  40. Segment(F', G') → h_1
  41. Angle(C', A', B') → α
  42. Angle(B', C', A') → β
  43. Angle(A', B', C') → γ
  44. Angle(B, C, A) → δ
  45. Angle(A, B, C) → ε
  46. Angle(C, A, B) → ζ

AI Drawing Prompt Reference

Draw a triangle and its scaled image with a specified center of dilation. Measure the side lengths and distances from the center for both the original and scaled triangles. Calculate and compare their areas to show the scaling factor. Label the interior angles of both triangles to demonstrate angle invariance under dilation. Also, draw rays from the center to the vertices of the original triangle and lines connecting the vertices of the scaled triangle.
The prompt above was compiled from the original drawing commands and is for reference only.