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Graphs Describing Motion - Task

Graphs Describing Motion - Task
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2017-06-19 02:55
TrigonometryCoordinate GeometryTransformationParametric Equation
This example demonstrates how to describe motion trajectories using graphs, focusing on parametric curves and geometric transformations. Key math concepts include parametric equations, coordinate geometry, geometric transformations, and triangle properties. Construction highlights involve commands like Line, Point, OrthogonalLine, Intersect, Polygon, Segment, RotateText in GeoGebra to build graphs, intersections, and transformed shapes. Suitable for high school and above, illustrating the application of parametric equations in motion description and the visual effects of geometric transformations.

GeoGebra Commands & Parameters

  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