MathPlotAI Logo MathPlotAI

Homothety and Symmetry

Homothety and Symmetry
Loading the math board and drawing, please wait…
2018-05-09 07:37
FunctionTransformationGeometric Construction
In collections Homothety, Rotation Symmetry -RO
This example demonstrates homothety and symmetry in geometric figures. Key mathematical concepts include homothety, reflection, and polynomial functions. Using GeoGebra commands such as Polygon, Segment, Dilate, and Mirror, complex geometric shapes can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. Segment(D, B) → j
  3. Midpoint(j) → E
  4. Polygon(C, A, B) → t1, b, c, a
  5. Point(j) → F
  6. Dilate(C, 5 / 6, F) → C'
  7. Dilate(A, 5 / 6, F) → A'
  8. Dilate(B, 5 / 6, F) → B'
  9. Polygon(C', A', B') → t1', b', c', a'
  10. Dilate(C', 5 / 6, F) → C''
  11. Dilate(A', 5 / 6, F) → A''
  12. Dilate(B', 5 / 6, F) → B''
  13. Polygon(C'', A'', B'') → t1'', b'', c'', a''
  14. Dilate(C'', 5 / 6, F) → C'''
  15. Dilate(A'', 5 / 6, F) → A'''
  16. Dilate(B'', 5 / 6, F) → B'''
  17. Polygon(C''', A''', B''') → t1''', b''', c''', a'''
  18. Dilate(C''', 5 / 6, F) → G
  19. Dilate(A''', 5 / 6, F) → H
  20. Dilate(B''', 5 / 6, F) → I
  21. Polygon(G, H, I) → t2, i_1, g_1, h_1
  22. Dilate(G, 5 / 6, F) → G'
  23. Dilate(H, 5 / 6, F) → H'
  24. Dilate(I, 5 / 6, F) → I'
  25. Polygon(G', H', I') → t2', i', g', h'
  26. Mirror(C, E) → C'_1
  27. Mirror(A, E) → A'_1
  28. Mirror(B, E) → B'_1
  29. Polygon(C'_1, A'_1, B'_1) → t1'_1, b'_1, c'_1, a'_1
  30. Mirror(C', E) → C''_1
  31. Mirror(A', E) → A''_1
  32. Mirror(B', E) → B''_1
  33. Polygon(C''_1, A''_1, B''_1) → t1''_1, b''_1, c''_1, a''_1
  34. Mirror(C'', E) → C'''_1
  35. Mirror(A'', E) → A'''_1
  36. Mirror(B'', E) → B'''_1
  37. Polygon(C'''_1, A'''_1, B'''_1) → t1'''_1, b'''_1, c'''_1, a'''_1
  38. Mirror(C''', E) → J
  39. Mirror(A''', E) → K
  40. Mirror(B''', E) → L
  41. Polygon(J, K, L) → t3, l, j_1, k
  42. Mirror(G, E) → G'_1
  43. Mirror(H, E) → H'_1
  44. Mirror(I, E) → I'_1
  45. Polygon(G'_1, H'_1, I'_1) → t2'_1, i'_1, g'_1, h'_1
  46. Mirror(G', E) → G''
  47. Mirror(H', E) → H''
  48. Mirror(I', E) → I''
  49. Polygon(G'', H'', I'') → t2'', i'', g'', h''

AI Drawing Prompt Reference

Draw a triangle with points A, B, and C, then perform a homothety with a ratio of 5/6 centered at point F to get triangle A'B'C'. Repeat the homothety with the same ratio centered at F to get triangle A''B''C''. Perform another homothety with the same ratio centered at F to get triangle A'''B'''C'''. Finally, perform a mirror transformation of A'''B'''C''' with respect to point F to get triangle JKL.
The prompt above was compiled from the original drawing commands and is for reference only.