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Rugby Conversion Kick Point Location

Rugby Conversion Kick Point Location
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2015-09-23 02:57
CircleGeometric ConstructionLocus
This example demonstrates how to determine the location of a rugby conversion kick point, involving concepts like circles, loci, and ratios. Construction uses GeoGebra commands such as Intersect, Locus, and OrthogonalLine. Suitable for high school students or math enthusiasts learning geometric construction and function graphing.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Polygon(A, B, C, D) → poly1, a, b, c, d
  3. Point(c) → TryLocation
  4. Segment((x(TryLocation), 50), (x(TryLocation), 100)) → kicksegment
  5. OrthogonalLine(TryLocation, c) → a_2
  6. Point(kicksegment) → KickSpot
  7. Vector(KickSpot, centreposts) → goaldirection
  8. OrthogonalLine(G, d) → e
  9. OrthogonalLine(F, d) → f
  10. OrthogonalLine(E, d) → g
  11. Intersect(e, b) → H
  12. Intersect(f, b) → I
  13. Intersect(g, b) → J
  14. Polygon(M, D, C, N) → poly2, m, d_1, c_1, n
  15. Polygon(A, K, L, B) → poly3, a_1, k, l, b_1
  16. Segment(O, A_1) → h
  17. Segment(P, B_1) → i
  18. Segment(Z, W) → j
  19. Segment(Q, U) → p
  20. Segment(R, V) → q
  21. Segment(T, S) → r
  22. Segment(D, C) → s
  23. Segment(F, I) → t_2
  24. Segment(A, B) → e_1
  25. Segment(M, K) → f_1
  26. Segment(K, L) → g_1
  27. Segment(L, N) → h_1
  28. Segment(N, M) → i_1
  29. Segment(C_1, D_1) → j_1
  30. Segment(G_1, H_1) → k_1
  31. Segment(I_1, J_1) → l_1
  32. Segment(E_1, F_1) → m_1
  33. Segment(L_1, K_1) → n_1
  34. Segment(N_1, M_1) → p_1
  35. Segment(Q_1, O_1) → q_1
  36. Segment(R_1, P_1) → r_1
  37. Segment(G, H) → s_1
  38. Segment(E, J) → t_1
  39. Segment(Q, KickSpot) → b_2
  40. Segment(KickSpot, R) → c_2
  41. Angle(R, KickSpot, Q) → α
  42. OrthogonalLine(centreposts, c) → centreline
  43. Segment(centreposts, TryLocation) → f_2
  44. Circle(Q, f_2) → g_2
  45. Intersect(g_2, centreline, 2) → centrecross
  46. Circle(centrecross, Q) → h_2
  47. OrthogonalLine(centrecross, centreline) → i_2
  48. Intersect(h_2, i_2) → W_1, BestSpot
  49. Locus(BestSpot, TryLocation) → loc1
  50. OrthogonalPlane(KickSpot, goaldirection) → o
  51. CornerThreeD(-1, 11) → S_1
  52. CornerThreeD(-1, 11) → EP
  53. CornerThreeD(-1, 1) → T_1
  54. CornerThreeD(-1, 2) → U_1
  55. CornerThreeD(-1, 3) → V_1
  56. CornerThreeD(-1, 4) → Z_1
  57. CornerThreeD(-1, 5) → A_2
  58. CornerThreeD(-1, 6) → B_2
  59. CornerThreeD(-1, 7) → C_2
  60. Midpoint(CornerThreeD[-1, 1], CornerThreeD[-1, 7]) → VCENTRE
  61. Vector(VCENTRE - EP) → VDIR
  62. UnitVector(VDIR) → UVDIR
  63. Circle(Q, R, KickSpot) → d_2
  64. Vector(KickSpot, Aimspot) → kickdir
  65. UnitVector(kickdir) → unitkickdir
  66. LaTeX(α, true, true) → text1
  67. CurveCartesian(xball(tt), yball(tt), zball(tt), tt, 0, maxt) → u_1
  68. Intersect(d_2, a_2) → Anglespot1, Anglespot2
  69. Segment(Q, Anglespot1) → j_2
  70. Segment(R, Anglespot1) → k_2
  71. Segment(R, Anglespot2) → l_2
  72. Segment(Q, Anglespot2) → m_2
  73. Polygon(Q, U, U + (0.3, 0), Q + (0.3, 0)) → q1, q_2, u_2, n_2, r_2
  74. Polygon(T, S, S + (0, 0, 0.3), T + (0, 0, 0.3)) → q2, s_2, e_2, f_3, i_3
  75. Polygon(R, V, V + (-0.3, 0), R + (-0.3, 0)) → q3, r_3, v_2, g_3, h_3

AI Drawing Prompt Reference

Draw a rugby field with try line, goal line, and center line. From the try point, draw a vertical line to the goal line to mark the kick spot. Create a circle centered at the kick spot intersecting the goal line at two points. Then, draw two lines perpendicular to the center line and the line connecting the kick spot to one of the circle's intersection points, finding their intersection as the best spot for a conversion kick.
The prompt above was compiled from the original drawing commands and is for reference only.