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Homothety and Reflection by Point

Homothety and Reflection by Point
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2018-05-09 07:07
FunctionCoordinate GeometryTransformation
In collections Homothety, Rotation Symmetry -RO
This example demonstrates homothety and reflection transformations. Key mathematical concepts include homothety and reflection. Using GeoGebra commands such as Polygon, Segment, Midpoint, Dilate, Mirror, etc., homothetic and reflected figures can be constructed. Suitable for students from middle school and above learning geometric transformations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. Segment(A, C) → j
  3. Midpoint(j) → E
  4. Point(j) → F
  5. Polygon(D, E, B, C) → q1, d, e, b, c
  6. Dilate(D, 5 / 6, F) → D'
  7. Dilate(E, 5 / 6, F) → E'
  8. Dilate(B, 5 / 6, F) → B'
  9. Dilate(C, 5 / 6, F) → C'
  10. Polygon(D', E', B', C') → q1', d', e', b', c'
  11. Dilate(D', 5 / 6, F) → D''
  12. Dilate(E', 5 / 6, F) → E''
  13. Dilate(B', 5 / 6, F) → B''
  14. Dilate(C', 5 / 6, F) → C''
  15. Polygon(D'', E'', B'', C'') → q1'', d'', e'', b'', c''
  16. Dilate(D'', 5 / 6, F) → D'''
  17. Dilate(E'', 5 / 6, F) → E'''
  18. Dilate(B'', 5 / 6, F) → B'''
  19. Dilate(C'', 5 / 6, F) → C'''
  20. Polygon(D''', E''', B''', C''') → q1''', d''', e''', b''', c'''
  21. Dilate(D''', 5 / 6, F) → G
  22. Dilate(E''', 5 / 6, F) → H
  23. Dilate(B''', 5 / 6, F) → I
  24. Dilate(C''', 5 / 6, F) → J
  25. Polygon(G, H, I, J) → q2, g_1, h_1, i_1, j_1
  26. Dilate(G, 5 / 6, F) → G'
  27. Dilate(H, 5 / 6, F) → H'
  28. Dilate(I, 5 / 6, F) → I'
  29. Dilate(J, 5 / 6, F) → J'
  30. Polygon(G', H', I', J') → q2', g', h', i', j'
  31. Mirror(D, E) → D'_1
  32. Mirror(E, E) → E'_1
  33. Mirror(B, E) → B'_1
  34. Mirror(C, E) → C'_1
  35. Polygon(D'_1, E'_1, B'_1, C'_1) → q1'_1, d'_1, e'_1, b'_1, c'_1
  36. Mirror(D', E) → D''_1
  37. Mirror(E', E) → E''_1
  38. Mirror(B', E) → B''_1
  39. Mirror(C', E) → C''_1
  40. Polygon(D''_1, E''_1, B''_1, C''_1) → q1''_1, d''_1, e''_1, b''_1, c''_1
  41. Mirror(D'', E) → D'''_1
  42. Mirror(E'', E) → E'''_1
  43. Mirror(B'', E) → B'''_1
  44. Mirror(C'', E) → C'''_1
  45. Polygon(D'''_1, E'''_1, B'''_1, C'''_1) → q1'''_1, d'''_1, e'''_1, b'''_1, c'''_1
  46. Mirror(D''', E) → K
  47. Mirror(E''', E) → L
  48. Mirror(B''', E) → M
  49. Mirror(C''', E) → N
  50. Polygon(K, L, M, N) → q3, k, l, m, n
  51. Mirror(G, E) → G'_1
  52. Mirror(H, E) → H'_1
  53. Mirror(I, E) → I'_1
  54. Mirror(J, E) → J'_1
  55. Polygon(G'_1, H'_1, I'_1, J'_1) → q2'_1, g'_1, h'_1, i'_1, j'_1
  56. Mirror(G', E) → G''
  57. Mirror(H', E) → H''
  58. Mirror(I', E) → I''
  59. Mirror(J', E) → J''
  60. Polygon(G'', H'', I'', J'') → q2'', g'', h'', i'', j''
  61. Dilate(G', 5 / 6, F) → G''_1
  62. Dilate(H', 5 / 6, F) → H''_1
  63. Dilate(I', 5 / 6, F) → I''_1
  64. Dilate(J', 5 / 6, F) → J''_1
  65. Polygon(G''_1, H''_1, I''_1, J''_1) → q2''_1, g''_1, h''_1, i''_1, j''_1
  66. Mirror(G''_1, E) → O
  67. Mirror(H''_1, E) → P
  68. Mirror(I''_1, E) → Q
  69. Mirror(J''_1, E) → R
  70. Polygon(O, P, Q, R) → q4, o, p, q, r
  71. Dilate(G''_1, 5 / 6, F) → S
  72. Dilate(H''_1, 5 / 6, F) → T
  73. Dilate(I''_1, 5 / 6, F) → U
  74. Dilate(J''_1, 5 / 6, F) → V
  75. Polygon(S, T, U, V) → q5, s, t, u, v
  76. Mirror(S, E) → S'
  77. Mirror(T, E) → T'
  78. Mirror(U, E) → U'
  79. Mirror(V, E) → V'
  80. Polygon(S', T', U', V') → q5', s', t', u', v'

AI Drawing Prompt Reference

Draw a quadrilateral ABCD, connect AC to find midpoint E, dilate D, E, B, C by a factor of 5/6 from E to get D', E', B', C'. Then dilate D', E', B', C' by 5/6 from E to get D'', E'', B'', C''. Dilate D'', E'', B'', C'' by 5/6 from E to get D''', E''', B''', C'''. Mirror D'', E'', B'', C'' about D and E to get D''_1, E''_1, B''_1, C''_1, and mirror D', E', B', C' to get D''''_1, E''''_1, B''''_1, C''''_1. Finally, mirror D, E to get K, L, M.
The prompt above was compiled from the original drawing commands and is for reference only.