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Element G Transformations

Element G Transformations
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2020-05-14 00:40
Coordinate GeometryTransformationGeometric Construction
This example demonstrates the construction of geometric figure G through transformations like rotation, intersection, and mirroring. It involves core math concepts including geometric transformations, coordinate geometry, similar triangles, and function graphs. GeoGebra commands used are Rotate, Intersect, Mirror, Line, Circle, etc. Suitable for high school mathematics teaching to understand the integration of geometric transformations and coordinate geometry.

GeoGebra Commands & Parameters

  1. Rotate(B, 67.5°, A) → B'
  2. Ray(A, B') → f
  3. Intersect(f, yAxis) → C
  4. Segment(C, A) → g
  5. Segment(C, B) → h
  6. Circle(C, 0.35) → c
  7. Intersect(c, g, 1) → D
  8. Intersect(c, h, 1) → E
  9. Line(A, yAxis) → i
  10. Line(B, yAxis) → j
  11. Line(D, E) → k
  12. Intersect(i, k) → F
  13. Intersect(k, j) → G
  14. Distance(F, A) → af1
  15. Mirror(F, H) → F'
  16. Segment(F, F') → l
  17. Mirror(F', yAxis) → F''
  18. Mirror(H, yAxis) → H'
  19. Segment(F, G) → m
  20. Segment(F', F'') → n
  21. Segment(G, F'') → p
  22. CircleArc(M, Q, I) → d
  23. CircleArc(M, O, Q) → e
  24. CircleArc(N, P, R) → r
  25. CircleArc(N, R, J) → q
  26. Line(A, zAxis) → s
  27. Intersect(s, d) → S,
  28. Line(B, zAxis) → t
  29. Intersect(t, q) → T,
  30. Segment(S, T) → a
  31. Segment(S, A) → b
  32. Segment(T, B) → f_1
  33. Plane(D, A, K) → p_1
  34. Surface(l, (straal * cos(t)) + y(H), (straal * sin(t)) + z(ver), l, ((-v2)) / 2, v2 / 2, t, 0°, 180°) → o
  35. PointIn(p_1) → V
  36. PointIn(p_1) → W
  37. PointIn(p_1) → Z
  38. PointIn(p_1) → A_1
  39. PointIn(p_1) → B_1
  40. Segment(C, A) → g_1
  41. Segment(E_1, C_1) → h_1
  42. Segment(E_1, D_1) → i_1
  43. Segment(E_1, C) → j_1
  44. Segment(U, D) → k_1
  45. Polygon(G_1, A_1, Z, H_1) → vierhoek1, l_1, a_1, z_1, m_1
  46. Polygon(F_1, U, A_1, G_1) → vierhoek2, n_1, u, q_1, r_1
  47. Polygon(H_1, Z, W, I_1) → vierhoek3, s_1, z_2, w, t_1
  48. Polygon(I_1, W, V, J_1) → vierhoek4, b_1, w_1, v, c_1
  49. Polygon(J_1, V, B_1, K_1) → vierhoek5, d_1, v_1, e_1, f_2
  50. Polygon(K_1, B_1, S, L_1) → vierhoek6, g_2, h_2, s_2, i_2
  51. Polygon(L_1, S, C_1, E_1) → vierhoek7, j_2, s_3, k_2, l_2
  52. Polygon(C, D, U, F_1) → vierhoek8, c_2, d_2, u_1, m_2
  53. Plane(C, (-C), C + ver) → sym
  54. Mirror(vierhoek1, sym) → vierhoek1'
  55. Mirror(vierhoek2, sym) → vierhoek2'
  56. Mirror(vierhoek3, sym) → vierhoek3'
  57. Mirror(vierhoek4, sym) → vierhoek4'
  58. Mirror(vierhoek5, sym) → vierhoek5'
  59. Mirror(vierhoek6, sym) → vierhoek6'
  60. Mirror(vierhoek7, sym) → vierhoek7'
  61. Mirror(vierhoek8, sym) → vierhoek8'
  62. Mirror(vierhoek1, sym2) → vierhoek1'_1
  63. Mirror(vierhoek2, sym2) → vierhoek2'_1
  64. Mirror(vierhoek3, sym2) → vierhoek3'_1
  65. Mirror(vierhoek4, sym2) → vierhoek4'_1
  66. Mirror(vierhoek5, sym2) → vierhoek5'_1
  67. Mirror(vierhoek6, sym2) → vierhoek6'_1
  68. Mirror(vierhoek7, sym2) → vierhoek7'_1
  69. Mirror(vierhoek8, sym2) → vierhoek8'_1
  70. Mirror(vierhoek1', sym2) → vierhoek1''
  71. Mirror(vierhoek2', sym2) → vierhoek2''
  72. Mirror(vierhoek3', sym2) → vierhoek3''
  73. Mirror(vierhoek4', sym2) → vierhoek4''
  74. Mirror(vierhoek5', sym2) → vierhoek5''
  75. Mirror(vierhoek6', sym2) → vierhoek6''
  76. Mirror(vierhoek7', sym2) → vierhoek7''
  77. Mirror(vierhoek8', sym2) → vierhoek8''
  78. Segment(U, A_1) → n_2
  79. Segment(A_1, Z) → p_2
  80. Segment(Z, W) → q_2
  81. Segment(W, V) → r_2
  82. Segment(V, B_1) → t_2
  83. Segment(B_1, S) → b_2
  84. Segment(C_1, S) → e_2
  85. Polygon(S, T, D_1, C_1) → vierhoek9, s_4, t_3, f_3, g_3
  86. Mirror(B_1, sym) → M_1
  87. Mirror(V, sym) → V'
  88. Mirror(W, sym) → W'
  89. Mirror(Z, sym) → Z'
  90. Mirror(A_1, sym) → N_1
  91. Mirror(U, sym) → U'
  92. Polygon(D, E, U', U) → vierhoek10, d_3, e_3, u', u_2
  93. Polygon(B_1, M_1, T, S) → vierhoek11, h_3, i_3, t_4, s_5
  94. Polygon(B_1, V, V', M_1) → vierhoek12, j_3, v_2, v', k_3
  95. Polygon(V, W, W', V') → vierhoek13, v_3, w_2, w', l_3
  96. Polygon(W, Z, Z', W') → vierhoek14, w_3, z_3, z', m_3
  97. Polygon(Z, A_1, N_1, Z') → vierhoek15, z_4, n_3, p_3, q_3
  98. Point(p_3) → O_1
  99. Polygon(A_1, U, U', N_1) → vierhoek16, r_3, a_3, b_3, c_3
  100. Segment(T, M_1) → f_4
  101. Segment(M_1, V') → g_4
  102. Segment(V', W') → h_4
  103. Segment(W', Z') → i_4
  104. Segment(Z', O_1) → j_4
  105. Segment(O_1, U') → k_4
  106. Mirror(vierhoek11, sym2) → vierhoek11'
  107. Mirror(vierhoek12, sym2) → vierhoek12'
  108. Mirror(vierhoek13, sym2) → vierhoek13'
  109. Mirror(vierhoek14, sym2) → vierhoek14'
  110. Mirror(vierhoek15, sym2) → vierhoek15'
  111. Mirror(vierhoek16, sym2) → vierhoek16'
  112. Mirror(vierhoek10, sym2) → vierhoek10'
  113. Mirror(U, sym2) → U'_1
  114. Mirror(D, sym2) → D'
  115. Segment(U'_1, D') → l_4
  116. Mirror(B_1, sym2) → P_1
  117. Mirror(V, sym2) → V'_1
  118. Mirror(W, sym2) → W'_1
  119. Mirror(Z, sym2) → Z'_1
  120. Mirror(A_1, sym2) → Q_1
  121. Mirror(Z', sym2) → Z''
  122. Mirror(O_1, sym2) → R_1
  123. Mirror(U', sym2) → U''
  124. Mirror(E, sym2) → E'
  125. Mirror(C, sym2) → C'
  126. Mirror(E_1, sym2) → S_1
  127. Mirror(W', sym2) → W''
  128. Mirror(V', sym2) → V''
  129. Mirror(M_1, sym2) → T_1
  130. Segment(T, T_1) → m_4
  131. Segment(T_1, V'') → n_4
  132. Segment(V'', W'') → p_4
  133. Segment(W'', Z'') → q_4
  134. Segment(Z'', R_1) → r_4
  135. Segment(R_1, U'') → a_4
  136. Segment(U'', E') → b_4
  137. Segment(S_1, C') → c_4
  138. Segment(S_1, D_1) → d_4
  139. Segment(S_1, C_1) → e_4
  140. Segment(S, P_1) → f_5
  141. Segment(P_1, V'_1) → g_5
  142. Segment(V'_1, W'_1) → h_5
  143. Segment(W'_1, Z'_1) → i_5
  144. Segment(Z'_1, Q_1) → j_5
  145. Segment(Q_1, U'_1) → k_5
  146. Segment(D', C') → l_5
  147. Segment(C', E') → m_5
  148. Polygon(D_1, E_1, C_1) → driehoek1, n_5, p_5, q_5
  149. Polygon(D_1, C_1, S_1) → driehoek2, r_5, t_5, a_5
  150. Segment(C, D) → b_5
  151. Segment(D, E) → c_5
  152. Segment(E, C) → d_5

AI Drawing Prompt Reference

Draw a geometric figure constructed through transformations like rotation, intersection, and mirroring. Rotate a point, create a ray intersecting the y-axis, connect the intersection with the origin. Draw a circle centered at the intersection, intersect it with line segments. Connect intersections, draw perpendicular lines, and form new segments by connecting points. Mirror a point, connect mirrored points with the origin. Finally, add circular arcs and quadrilaterals to showcase the integration of geometric transformations and coordinate geometry.
The prompt above was compiled from the original drawing commands and is for reference only.