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Graphs of Motion

Graphs of Motion
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2017-11-19 02:36
FunctionCoordinate GeometryParametric EquationInequalityGraphing
This example demonstrates the graphical representation of motion, including trajectories and velocity changes, through dynamic graphs. Key mathematical concepts involve functions, inequalities, parametric equations, and coordinate geometry. Construction highlights GeoGebra commands like Line, Point, OrthogonalLine, Intersect, Polygon, Segment, and RotateText. Ideal for high school students and enthusiasts exploring kinematics and graphical methods in mathematics.

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
  66. Intersect(d_5, yAxis) → T
  67. Intersect(e_3, i_3) → W_1
  68. Intersect(yAxis, e_3) → Z_1
  69. Polygon((0, -8), (21, -8), (21, 22), (0, 22)) → q1, k_3, l_3, m_3, n_3
  70. Segment(T, Z_1) → j_3

AI Drawing Prompt Reference

Draw a dynamic graph showing motion with trajectories and velocity changes. Start by plotting the x and y axes, then create a line segment on the x-axis and draw perpendicular lines to it. Find the intersections of these lines and connect the points to form polygons. Also, draw some horizontal line segments and locate their intersections. Finally, connect these intersection points to complete the graph.
The prompt above was compiled from the original drawing commands and is for reference only.