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反射、旋转、缩放和平移 by Robyn Porter (2)

反射、旋转、缩放和平移 by Robyn Porter (2)
几何画板及绘图内容加载中，请稍等……
2019-07-22 00:18
解析几何变换几何作图
①本范例演示了几何图形的反射、旋转、缩放和平移变换；②涉及的核心数学概念包括变换、对称性、坐标几何；③作图要点——使用了Intersect, Point, Circle, Segment, Polygon, Rotate, Vector, Translate, Mirror, Dilate, Midpoint等GeoGebra命令和对象；④适合高中数学教学和几何变换学习。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Point(yAxis) → B
  3. Circle(A, B) → c
  4. Segment(A, C) → a
  5. Segment(C, D) → b
  6. Segment(D, E) → d
  7. Segment(E, A) → e
  8. Polygon(A, C, D, E) → poly1, a_1, c_1, d_1, e_1
  9. Rotate(A, Windmill, A) → A'
  10. Rotate(C, Windmill, A) → C'
  11. Rotate(D, Windmill, A) → D'
  12. Rotate(E, Windmill, A) → E'
  13. Polygon(A', C', D', E') → poly1', a', c', d', e'
  14. Polygon(A, F, G, H) → poly2, a_2, f, g, h
  15. Polygon(A, I, J, K) → poly3, a_3, i, j, k
  16. Polygon(A, L, M, N) → poly4, a_4, l, m, n
  17. Rotate(A, Windmill, A) → A'_1
  18. Rotate(F, Windmill, A) → F'
  19. Rotate(G, Windmill, A) → G'
  20. Rotate(H, Windmill, A) → H'
  21. Polygon(A'_1, F', G', H') → poly2', a'_1, f', g', h'
  22. Rotate(A, Windmill, A) → A'_2
  23. Rotate(I, Windmill, A) → I'
  24. Rotate(J, Windmill, A) → J'
  25. Rotate(K, Windmill, A) → K'
  26. Polygon(A'_2, I', J', K') → poly3', a'_2, i', j', k'
  27. Rotate(A, Windmill, A) → A'_3
  28. Rotate(L, Windmill, A) → L'
  29. Rotate(M, Windmill, A) → M'
  30. Rotate(N, Windmill, A) → N'
  31. Polygon(A'_3, L', M', N') → poly4', a'_3, l', m', n'
  32. Polygon(A, O, P, Q, R) → poly5, a_5, o, p, q, r_3
  33. Polygon(S, T, U, V) → poly6, s, t, u, v
  34. Circle(W, Z) → f_1
  35. Polygon(A_1, B_1, K_1, L_1, C_1, D_1, E_1, F_1, G_1, H_1, I_1, J_1) → poly7, a_6, j_1, k_1, l_1, b_1, c_2, d_2, e_2, f_2, g_1, h_1, i_1
  36. Polygon(M_1, N_1, W_1, Z_1, A_2, B_2, C_2, O_1, P_1, Q_1, R_1, S_1, T_1, U_1, V_1) → poly8, m_1, v_1, w_1, z_1, a_7, b_2, c_3, n_1, o_1, p_1, q_1, r_1, s_1, t_1, u_1
  37. Point(Circle[A, Clouds]) → E_2
  38. Segment(A, E_2) → g_2
  39. Vector(A, E_2) → z
  40. Translate(A_1, z) → F_2
  41. Translate(B_1, z) → G_2
  42. Translate(C_1, z) → H_2
  43. Translate(D_1, z) → I_2
  44. Translate(E_1, z) → J_2
  45. Translate(F_1, z) → K_2
  46. Translate(G_1, z) → L_2
  47. Translate(H_1, z) → M_2
  48. Translate(I_1, z) → N_2
  49. Translate(J_1, z) → O_2
  50. Translate(K_1, z) → P_2
  51. Translate(L_1, z) → Q_2
  52. Polygon(F_2, G_2, P_2, Q_2, H_2, I_2, J_2, K_2, L_2, M_2, N_2, O_2) → poly7', f_3, o_2, p_2, q_2, g_3, h_2, i_2, j_2, k_2, l_2, m_2, n_2
  53. Translate(M_1, z) → R_2
  54. Translate(N_1, z) → S_2
  55. Translate(O_1, z) → T_2
  56. Translate(P_1, z) → U_2
  57. Translate(Q_1, z) → V_2
  58. Translate(R_1, z) → W_2
  59. Translate(S_1, z) → Z_2
  60. Translate(T_1, z) → A_3
  61. Translate(U_1, z) → B_3
  62. Translate(V_1, z) → C_3
  63. Translate(W_1, z) → D_3
  64. Translate(Z_1, z) → E_3
  65. Translate(A_2, z) → F_3
  66. Translate(B_2, z) → G_3
  67. Translate(C_2, z) → H_3
  68. Polygon(R_2, S_2, D_3, E_3, F_3, G_3, H_3, T_2, U_2, V_2, W_2, Z_2, A_3, B_3, C_3) → poly8', r_2, c_4, d_3, e_3, f_4, g_4, h_3, s_2, t_2, u_2, v_2, w_2, z_2, a_8, b_3
  69. Point(s) → D_2
  70. Point(s) → I_4
  71. Polygon(D_2, G_4, H_4, I_4) → poly12, d_5, g_5, h_4, i_4
  72. Point(h_4) → M_4
  73. Polygon(H_4, J_4, K_4, L_4, M_4) → poly13, h_5, j_4, k_4, l_5, m_4
  74. Mirror(H_4, h_4) → N_4
  75. Mirror(J_4, h_4) → O_4
  76. Mirror(K_4, h_4) → P_4
  77. Mirror(L_4, h_4) → Q_4
  78. Mirror(M_4, h_4) → R_4
  79. Polygon(N_4, O_4, P_4, Q_4, R_4) → poly13', n_4, o_4, p_3, q_4, r_4
  80. Point(s) → T_4
  81. Point(s) → U_4
  82. Polygon(S_4, T_4, U_4, V_4) → poly14, s_4, t_4, u_4, v_4
  83. Polygon(W_4, Z_4, A_5, B_5, C_5, D_5, E_5, F_5, G_5, H_5) → poly15, w_4, h_6, z_4, a_{10}, b_5, c_6, d_6, e_5, f_6, g_6
  84. Point(h_6) → I_5
  85. Dilate(W_4, Balloon, I_5) → J_5
  86. Dilate(Z_4, Balloon, I_5) → K_5
  87. Dilate(A_5, Balloon, I_5) → L_5
  88. Dilate(B_5, Balloon, I_5) → M_5
  89. Dilate(C_5, Balloon, I_5) → N_5
  90. Dilate(D_5, Balloon, I_5) → O_5
  91. Dilate(E_5, Balloon, I_5) → P_5
  92. Dilate(F_5, Balloon, I_5) → Q_5
  93. Dilate(G_5, Balloon, I_5) → R_5
  94. Dilate(H_5, Balloon, I_5) → S_5
  95. Polygon(J_5, K_5, L_5, M_5, N_5, O_5, P_5, Q_5, R_5, S_5) → poly15', j_5, s_5, k_5, l_6, m_5, n_5, o_5, p_5, q_5, r_5
  96. Segment(S_4, J_5) → b_6
  97. Segment(V_4, S_5) → e_6
  98. Point(n_5) → V_5
  99. Segment(L_5, Q_5) → j_6
  100. Midpoint(v_4) → I_3
  101. Point(v_4) → J_3
  102. Point(v_4) → K_3
  103. Segment(L_5, J_3) → i_3
  104. Segment(I_3, V_5) → j_3
  105. Segment(K_3, Q_5) → k_3