MathPlotAI Logo MathPlotAI

Homothety and Reflection Point

Homothety and Reflection Point
Loading the math board and drawing, please wait…
2018-05-09 07:02
Coordinate GeometryCalculusTransformationGeometric Construction
In collections Homothety, Rotation Symmetry -RO
This example demonstrates the geometric relationship between homothety and reflection points. The core mathematical concepts involved include homothety, reflection, similar triangles, and coordinate geometry. The construction utilizes GeoGebra commands and objects such as Polygon, Segment, Midpoint, Point, Dilate, and Mirror. It is suitable for high school students studying geometric transformations and calculus.

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. Segment(A, C) → k
  5. Polygon(D, B, C) → t1, c, d, b
  6. Point(k) → F
  7. Dilate(D, 5 / 6, F) → D'
  8. Dilate(B, 5 / 6, F) → B'
  9. Dilate(C, 5 / 6, F) → C'
  10. Polygon(D', B', C') → t1', c', d', b'
  11. Dilate(D', 5 / 6, F) → D''
  12. Dilate(B', 5 / 6, F) → B''
  13. Dilate(C', 5 / 6, F) → C''
  14. Polygon(D'', B'', C'') → t1'', c'', d'', b''
  15. Dilate(D'', 5 / 6, F) → D'''
  16. Dilate(B'', 5 / 6, F) → B'''
  17. Dilate(C'', 5 / 6, F) → C'''
  18. Polygon(D''', B''', C''') → t1''', c''', d''', b'''
  19. Dilate(D''', 5 / 6, F) → G
  20. Dilate(B''', 5 / 6, F) → H
  21. Dilate(C''', 5 / 6, F) → I
  22. Polygon(G, H, I) → t2, i_1, g_1, h_1
  23. Dilate(G, 5 / 6, F) → G'
  24. Dilate(H, 5 / 6, F) → H'
  25. Dilate(I, 5 / 6, F) → I'
  26. Polygon(G', H', I') → t2', i', g', h'
  27. Polygon(J, K, 4) → poly2, l, m, n, p, L, M
  28. Segment(K, M) → q
  29. Midpoint(q) → N
  30. Segment(J, L) → r
  31. Point(r) → O
  32. Polygon(M, L, K) → t3, k_1, m_1, l_1
  33. Dilate(M, 5 / 6, O) → M'
  34. Dilate(L, 5 / 6, O) → L'
  35. Dilate(K, 5 / 6, O) → K'
  36. Polygon(M', L', K') → t3', k', m', l'
  37. Dilate(M', 5 / 6, O) → M''
  38. Dilate(L', 5 / 6, O) → L''
  39. Dilate(K', 5 / 6, O) → K''
  40. Polygon(M'', L'', K'') → t3'', k'', m'', l''
  41. Dilate(M'', 5 / 6, O) → M'''
  42. Dilate(L'', 5 / 6, O) → L'''
  43. Dilate(K'', 5 / 6, O) → K'''
  44. Polygon(M''', L''', K''') → t3''', k''', m''', l'''
  45. Dilate(M''', 5 / 6, O) → P
  46. Dilate(L''', 5 / 6, O) → Q
  47. Dilate(K''', 5 / 6, O) → R
  48. Polygon(P, Q, R) → t4, r_1, p_1, q_1
  49. Dilate(P, 5 / 6, O) → P'
  50. Dilate(Q, 5 / 6, O) → Q'
  51. Dilate(R, 5 / 6, O) → R'
  52. Polygon(P', Q', R') → t4', r', p', q'
  53. Dilate(P', 5 / 6, O) → P''
  54. Dilate(Q', 5 / 6, O) → Q''
  55. Dilate(R', 5 / 6, O) → R''
  56. Polygon(P'', Q'', R'') → t4'', r'', p'', q''
  57. Dilate(P'', 5 / 6, O) → P'''
  58. Dilate(Q'', 5 / 6, O) → Q'''
  59. Dilate(R'', 5 / 6, O) → R'''
  60. Polygon(P''', Q''', R''') → t4''', r''', p''', q'''
  61. Dilate(P''', 5 / 6, O) → S
  62. Dilate(Q''', 5 / 6, O) → T
  63. Dilate(R''', 5 / 6, O) → U
  64. Polygon(S, T, U) → t5, u, s, t
  65. Dilate(S, 5 / 6, O) → S'
  66. Dilate(T, 5 / 6, O) → T'
  67. Dilate(U, 5 / 6, O) → U'
  68. Polygon(S', T', U') → t5', u', s', t'
  69. Dilate(S', 5 / 6, O) → S''
  70. Dilate(T', 5 / 6, O) → T''
  71. Dilate(U', 5 / 6, O) → U''
  72. Polygon(S'', T'', U'') → t5'', u'', s'', t''
  73. Mirror(M, N) → M'_1
  74. Mirror(L, N) → L'_1
  75. Mirror(K, N) → K'_1
  76. Polygon(M'_1, L'_1, K'_1) → t3'_1, k'_1, m'_1, l'_1
  77. Mirror(M', N) → M''_1
  78. Mirror(L', N) → L''_1
  79. Mirror(K', N) → K''_1
  80. Polygon(M''_1, L''_1, K''_1) → t3''_1, k''_1, m''_1, l''_1
  81. Mirror(M'', N) → M'''_1
  82. Mirror(L'', N) → L'''_1
  83. Mirror(K'', N) → K'''_1
  84. Polygon(M'''_1, L'''_1, K'''_1) → t3'''_1, k'''_1, m'''_1, l'''_1
  85. Mirror(M''', N) → V
  86. Mirror(L''', N) → W
  87. Mirror(K''', N) → Z
  88. Polygon(V, W, Z) → t6, z_1, v, w
  89. Mirror(P, N) → P'_1
  90. Mirror(Q, N) → Q'_1
  91. Mirror(R, N) → R'_1
  92. Polygon(P'_1, Q'_1, R'_1) → t4'_1, r'_1, p'_1, q'_1
  93. Mirror(P', N) → P''_1
  94. Mirror(Q', N) → Q''_1
  95. Mirror(R', N) → R''_1
  96. Polygon(P''_1, Q''_1, R''_1) → t4''_1, r''_1, p''_1, q''_1
  97. Mirror(P'', N) → P'''_1
  98. Mirror(Q'', N) → Q'''_1
  99. Mirror(R'', N) → R'''_1
  100. Polygon(P'''_1, Q'''_1, R'''_1) → t4'''_1, r'''_1, p'''_1, q'''_1
  101. Mirror(P''', N) → A_1
  102. Mirror(Q''', N) → B_1
  103. Mirror(R''', N) → C_1
  104. Polygon(A_1, B_1, C_1) → t7, c_1, a_1, b_1
  105. Mirror(S, N) → S'_1
  106. Mirror(T, N) → T'_1
  107. Mirror(U, N) → U'_1
  108. Polygon(S'_1, T'_1, U'_1) → t5'_1, u'_1, s'_1, t'_1
  109. Mirror(S', N) → S''_1
  110. Mirror(T', N) → T''_1
  111. Mirror(U', N) → U''_1
  112. Polygon(S''_1, T''_1, U''_1) → t5''_1, u''_1, s''_1, t''_1
  113. Mirror(S'', N) → S'''
  114. Mirror(T'', N) → T'''
  115. Mirror(U'', N) → U'''
  116. Polygon(S''', T''', U''') → t5''', u''', s''', t'''