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Timed Coordinates Boat Game

Timed Coordinates Boat Game
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2015-06-24 16:35
TrigonometryCoordinate GeometryComplex NumberOptimizationGeometric Construction
This example demonstrates a coordinate geometry game enhanced with a timer for added challenge, helping learners grasp coordinate systems. Core math concepts include coordinate geometry, complex numbers, trapezoids, linear programming or optimization, sine functions, and right triangles. Construction highlights the use of GeoGebra commands like Random, Circle, Ray, OrthogonalLine, Intersect, CircumcircleArc, Midpoint, Sequence, If, Segment, Polygon, Line, Rotate, Mod, Point, and Textfield; objects such as O, bb, aa, cc, C_1, α, K, A, yA, xA, rr, A', v, c', a, b, B, C, D, T, d, E, F_2, e, f, G, H, g, I, h, liste3, dist, xB, yB, J, k, liste4, ang, raz, L. Suitable for high school students studying coordinate geometry and optimization problems.

GeoGebra Commands & Parameters

  1. Random(-10, 10) → bb
  2. Random(-10, 10) → aa
  3. Random(-10, 10) → cc
  4. Random(4, 15) → rr
  5. Circle(A, (((1.5 * v) - 1) * rr)) → c'
  6. Ray(A, (0, 0)) → a
  7. OrthogonalLine(A, a) → b
  8. Intersect(c', b) → B, C
  9. Intersect(c', a) → D, T
  10. CircumcircleArc(B, D, C) → d
  11. Midpoint(C, D) → E
  12. Midpoint(B, D) → F_2
  13. Ray(A', E) → e
  14. Ray(A', F_2) → f
  15. Intersect(d, e) → G,
  16. Intersect(d, f) → H,
  17. CircumcircleArc(G, D, H) → g
  18. Circle(I, 1) → h
  19. Sequence(Text[If[s < 10, " ", ""] + (s), (21.6 + (2 * Mod[s - 1, 3]), 7.75 - (2 * Div[s - 1, 3]))], s, 1, 12) → liste3
  20. Circle(J, 1) → k
  21. Sequence(Text[If[s ≟ 1, " ", If[s < 5, " ", ""]] + ((30 * (s - 1))) + "º", (21.25 + (2 * Mod[s - 1, 3]), (-6.25) - (2 * Div[s - 1, 3]))], s, 1, 12) → liste4
  22. If(yB > (-5), 5*°, ((((xB - (3 * yB)) / 2 - 19 - 1) * 30))°) → ang
  23. If(ang ≟ α ∧ dist ≟ rr, true, false) → raz
  24. Segment(O, N) → m
  25. Circle(A, (((2 * v) - 1) * rr) - n) → p
  26. Sequence(Circle[A, (((1.5 * v) - 1) * rr) - i], i, 0, n, n / 10) → liste5
  27. Polygon(P, Q, R, S) → poly1, p_1, q, r_1, s
  28. Circle((0, 0), If[((2 * v) * rr) > 12, 0, ((2 * v) * rr)]) → c
  29. Midpoint(K, L) → U
  30. Midpoint(U, L) → V
  31. Midpoint(U, V) → W
  32. Midpoint(V, L) → Z
  33. Segment(K, C_1) → l
  34. Line(A, l) → i
  35. Segment(A, U) → t
  36. Intersect(c, t) → A_1, B_1
  37. Segment(U, A_1) → a_1
  38. Rotate(C_1, (6 * v), U) → L'
  39. Segment(U, L') → b_1
  40. Mod((v * 100), 2) → ab
  41. Segment(O, D_1) → j
  42. Circle(O, C_1) → g_1
  43. Point(g_1) → E_1
  44. Segment(O, E_1) → h_1
  45. Circle(F_1, 6.5 - abs(r / 4.5)) → q_1
  46. Line(F_1, l) → i_1
  47. Intersect(q_1, i_1) → G_1, H_1
  48. Line(J_1, r_1) → j_1
  49. Point(j_1) → N_1
  50. Line(N_1, l) → l_1
  51. Line(J_1, l) → m_1
  52. Point(m_1) → O_1
  53. Point(l_1) → P_1
  54. Intersect(l_1, r_1) → M_1
  55. Polygon(M_1, N_1, J_1, F) → poly2, m_2, n_1, j_2, f_2
  56. Point(l_1) → Q_1
  57. Point(m_1) → R_1
  58. Polygon(P_1, Q_1, R_1, O_1) → poly3, p_2, q_2, r_2, o_1
  59. Point(j_1) → S_1
  60. Polygon(S_1, T_1, O_1, J_1) → poly4, s_1, t_1, o_2, j_3
  61. Midpoint(s_1) → V_1
  62. Midpoint(o_2) → W_1
  63. Midpoint(S_1, J_1) → Z_1
  64. Midpoint(t_1) → A_2
  65. Segment(V_1, W_1) → a_2
  66. Segment(Z_1, A_2) → b_2
  67. Intersect(b_2, a_2) → B_2
  68. Circle(B_2, V_1) → c_2
  69. Sequence((x(O) + i, y(D_1)), i, -11, 11, 1) → liste1
  70. Sequence((x(N) + i, y(N)), i, -11, 11, 1) → liste6
  71. Sequence((x(C_1), y(C_1) + i), i, -11, 11, 1) → liste7
  72. Sequence((x(E_1), y(E_1) + i), i, -11, 11, 1) → liste8
  73. Ray(M_1, T_1) → c_1
  74. Sequence(Segment[Element[liste8, i], Element[liste7, i]], i, 0, 22) → liste10
  75. Sequence((x(D_1) + i, 0), i, -11, 11) → liste2
  76. Sequence(Segment[Element[liste1, i], Element[liste6, i]], i, 0, 22) → liste9
  77. Line(S, P) → d_1
  78. Line(J_1, S_1) → e_1
  79. Line(Q_1, e_1) → f_1
  80. Intersect(d_1, s) → M
  81. Intersect(d_1, f_1) → C_2
  82. Line(R, d_1) → k_1
  83. Intersect(e_1, k_1) → D_2
  84. Polygon(S, C_2, Q_1, S_1, D_2, R) → poly5, s_2, c_3, q_3, s_3, d_2, r_3
  85. Point(d_1) → E_2
  86. Line(E_2, p_1) → e_2
  87. Intersect(k_1, e_2) → G_2
  88. Polygon(E_2, P, Q, G_2) → poly6, e_3, p_3, q_4, g_2
  89. Sequence(O + (i, 0), i, -10, 10) → liste11
  90. Sequence(O + (0, i), i, -10, 10) → liste12
  91. Sequence(i, i, -10, 10) → liste13
  92. Sequence(Text[Element[liste13, i], (x(Element[liste11, i] - 0.42), y(Element[liste11, i] - 0.85))], i, 1, Length[liste13], 2) → liste14
  93. Sequence(Text[Element[liste13, i], (x(Element[liste12, i] - 1), y(Element[liste12, i] - 0.31))], i, 1, Length[liste13], 2) → liste15
  94. Textfield(o) → inputBox1
  95. Textfield(r) → inputBox2
  96. Textfield(timelimit) → inputBox3