Soccer 3v3 - Positioning, Angles, and Dilations

Soccer 3v3 - Positioning, Angles, and Dilations
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2020-07-09 21:02
This example demonstrates the geometric principles of positioning, angles, and dilations used in soccer games. It involves core math concepts like angles, dilation, geometric transformations, similarity, and coordinate geometry. GeoGebra commands and objects such as Point, Line, Midpoint, Circle, Segment, Distance, Intersect, and Polygon are utilized in the construction. Suitable for high school mathematics education to understand geometric applications in sports.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Line(A, B) → f
  3. Point(f) → C
  4. Point(f) → D
  5. Point(f) → E
  6. Point(f) → F
  7. Midpoint(E, F) → Goal
  8. Circle(Goal, OffenseA) → c
  9. Point(Circle[OffenseA, 2]) → K
  10. Segment(OffenseA, K) → h
  11. Midpoint(OffenseA, K) → L
  12. Point(Circle[Goalkeeper, 2]) → N
  13. Segment(Goalkeeper, N) → j
  14. Midpoint(Goalkeeper, N) → M
  15. Distance(L, M) → distanceLM
  16. Distance(L, M) → d
  17. Distance(M, Goal) → distanceMGoal
  18. Point(Circle[OffenseB, 2]) → V
  19. Segment(OffenseB, V) → r
  20. Midpoint(OffenseB, V) → G
  21. Point(Circle[DefenderA, 2]) → S
  22. Segment(DefenderA, S) → t
  23. Midpoint(DefenderA, S) → B_1
  24. Line(V, DefenderA) → p_2
  25. Line(V, S) → q_2
  26. Line(V, Goalkeeper) → a_2
  27. Line(V, N) → b_2
  28. Point(p_2) → O_1
  29. Point(a_2) → U_1
  30. Line(O_1, f) → c_2
  31. Line(U_1, f) → e_2
  32. Intersect(q_2, c_2) → V_1
  33. Intersect(e_2, b_2) → Z_1
  34. Polygon(U_1, Z_1, V) → t8, v_2, u_1, z_1
  35. Polygon(O_1, V_1, V) → t9, v_3, g_3, h_3
  36. Midpoint(O_1, V_1) → H_2
  37. Midpoint(U_1, Z_1) → J_2
  38. Polygon(V, OffenseA, K) → t11, k_3, v_5, offensea
  39. Polygon(V, E, F) → t12, f_4, v_6, e_3
  40. Line(K, DefenderA) → i_3
  41. Line(K, S) → j_3
  42. Line(K, Goalkeeper) → n_3
  43. Line(K, N) → p_3
  44. Point(i_3) → Q
  45. Point(n_3) → R
  46. Line(Q, f) → n
  47. Line(R, f) → q_3
  48. Intersect(n, j_3) → B_2
  49. Intersect(q_3, p_3) → C_2
  50. Intersect(f, i_3) → E_2
  51. Intersect(f, j_3) → F_2
  52. Intersect(f, n_3) → G_2
  53. Intersect(f, p_3) → K_2
  54. Midpoint(Q, B_2) → A_1
  55. Midpoint(R, C_2) → N_2
  56. Polygon(Q, B_2, K) → t14, k_5, q_4, a_3
  57. Polygon(R, C_2, K) → t15, c_3, d_3, g_4
  58. Polygon(K, V, OffenseB) → t17, i_4, k_7, v_7
  59. Polygon(K, E, F) → t18, f_5, k_8, e_4
  60. Point(Circle[OffenseC, 2]) → T
  61. Segment(OffenseC, T) → g
  62. Midpoint(OffenseC, T) → P
  63. Polygon(K, OffenseC, T) → t1, t_1, k, offensec
  64. Polygon(V, OffenseC, T) → t2, t_2, v, i
  65. Point(Circle[DefenderC, 2]) → Z
  66. Segment(DefenderC, Z) → l
  67. Line(K, DefenderC) → m
  68. Line(K, Z) → p
  69. Point(m) → O
  70. Line(O, f) → s
  71. Intersect(s, p) → U
  72. Midpoint(O, U) → D_1
  73. Midpoint(DefenderC, Z) → E_1
  74. Polygon(O, U, K) → t3, k_1, o, u
  75. Intersect(f, m) → F_1
  76. Intersect(f, p) → G_1
  77. Line(V, DefenderC) → a
  78. Line(V, Z) → b
  79. Intersect(f, a) → H_1
  80. Intersect(f, b) → I_1
  81. Point(a) → J_1
  82. Line(J_1, f) → e
  83. Intersect(e, b) → M_1
  84. Midpoint(J_1, M_1) → N_1
  85. Polygon(J_1, M_1, V) → t4, v_1, j_1, m_1
  86. Line(T, DefenderA) → f_1
  87. Line(T, S) → g_1
  88. Line(T, DefenderC) → h_1
  89. Line(T, Z) → i_1
  90. Line(T, Goalkeeper) → l_1
  91. Line(T, N) → n_1
  92. Point(f_1) → W
  93. Point(h_1) → C_1
  94. Point(l_1) → P_1
  95. Line(W, f) → p_1
  96. Line(C_1, f) → q_1
  97. Line(P_1, f) → r_1
  98. Intersect(p_1, g_1) → Q_1
  99. Intersect(q_1, i_1) → R_1
  100. Intersect(n_1, r_1) → S_1
  101. Midpoint(P_1, S_1) → T_1
  102. Midpoint(W, Q_1) → W_1
  103. Midpoint(C_1, R_1) → A_2
  104. Polygon(T, V, OffenseB) → t5, offenseb, t_3, v_4
  105. Polygon(T, OffenseA, K) → t6, k_2, t_4, s_1
  106. Polygon(T, E, F) → t7, f_2, t_5, e_1
  107. Polygon(P_1, S_1, T) → t10, t_6, c_1, d_1
  108. Polygon(C_1, R_1, T) → t13, t_7, g_2, h_2
  109. Polygon(W, Q_1, T) → t16, t_8, w_1, i_2

AI Drawing Prompt Reference

Draw a 3v3 soccer formation on a field, including three attackers, a goalkeeper, and three defenders. Use circles to represent player positions and lines to connect relevant points, showing key angles and distances. Start by drawing a baseline, then determine the goal position and player positions, then draw the distances and angles between players, and finally connect relevant points with polygons to form areas.
The prompt above was compiled from the original drawing commands and is for reference only.