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运动描述的图形-任务

运动描述的图形-任务
几何画板及绘图内容加载中，请稍等……
2017-06-19 02:55
三角函数解析几何变换参数方程
①本范例演示如何通过图形描述运动轨迹，特别是参数曲线和几何变换的应用；②涉及核心数学概念包括参数方程、解析几何、几何变换和三角形性质；③作图要点：使用Line, Point, OrthogonalLine, Intersect, Polygon, Segment, RotateText等GeoGebra命令构建图形，如绘制直线、点、正交线、交点、多边形和旋转文本；④适合高中及以上学生，用于理解参数方程在运动描述中的应用及几何变换的视觉效果。

GeoGebra 命令及参数

  1. Line(C, xAxis) → i
  2. Line(D, i) → j
  3. Point(i) → E
  4. OrthogonalLine(E, i) → k
  5. Intersect(j, k) → F
  6. Point(i) → H
  7. OrthogonalLine(H, i) → l
  8. Point(l) → I
  9. OrthogonalLine(I, l) → q
  10. Point(l) → J
  11. OrthogonalLine(J, l) → r
  12. Point(q) → L
  13. OrthogonalLine(L, q) → s
  14. Intersect(s, r) → M
  15. Polygon(I, L, M, J) → poly1, i_1, l_1, m_1, j_1
  16. Intersect(i, l_1) → N
  17. Intersect(j, l_1) → O
  18. Intersect(j_1, j) → P
  19. Segment(H, N) → t_1
  20. Segment(P, O) → c
  21. Intersect(d, i_1) → Q
  22. Intersect(m_1, d) → R
  23. Segment(Q, R) → e
  24. Line(e_2, xAxis) → b
  25. Line(c_1, xAxis) → k_1
  26. Line(g_4, xAxis) → n_1
  27. Line(a_3, xAxis) → i_2
  28. Line(b_5, xAxis) → j_2
  29. Line(f_4, xAxis) → k_2
  30. Point(yAxis) → A_1
  31. OrthogonalLine(A_1, yAxis) → l_2
  32. Point(yAxis) → B_1
  33. OrthogonalLine(B_1, yAxis) → m_2
  34. Point(m_2) → C_1
  35. OrthogonalLine(C_1, m_2) → n_2
  36. Point(m_2) → D_1
  37. OrthogonalLine(D_1, m_2) → p_2
  38. Intersect(n_2, l_2) → E_1
  39. Intersect(p_2, l_2) → F_1
  40. Polygon(D_1, C_1, E_1, F_1) → poly2, d_5, c_2, e_3, f_5
  41. Intersect(i_2, n_2) → G_1
  42. Intersect(j_2, n_2) → H_1
  43. Intersect(b, n_2) → I_1
  44. Intersect(xAxis, n_2) → J_1
  45. Intersect(k_1, n_2) → K_1
  46. Intersect(k_2, n_2) → L_1
  47. Intersect(n_1, n_2) → M_1
  48. Intersect(n_1, p_2) → N_1
  49. Intersect(k_2, p_2) → O_1
  50. Intersect(k_1, p_2) → P_1
  51. Intersect(xAxis, b) → Q_1
  52. Intersect(xAxis, p_2) → R_1
  53. Intersect(b, j_2) → S_1
  54. Intersect(j_2, p_2) → T_1
  55. Intersect(b, p_2) → U_1
  56. Intersect(i_2, p_2) → V_1
  57. Segment(V_1, G_1) → q_2
  58. Segment(T_1, H_1) → r_2
  59. Segment(U_1, I_1) → s_2
  60. Segment(R_1, J_1) → t_2
  61. Segment(P_1, K_1) → a_2
  62. Segment(O_1, L_1) → b_2
  63. Segment(N_1, M_1) → h_3
  64. Segment(F_1, E_1) → i_3
  65. RotateText("position", 90°) → text4