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Equation Balance Demo

Equation Balance Demo
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2015-04-29 01:10
InequalityGeometric ConstructionGraphing
This example demonstrates interactive equation balancing through GeoGebra tools. It involves core math concepts like equation solving, inequalities, arithmetic operations, frequency distribution, continuity, LCM, and GCD. Constructed using commands like Segment, Point, CountIf, Circle, OrthogonalLine, Polygon, and Sum, it is suitable for high school and above students to explore mathematical applications of equation balancing.

GeoGebra Commands & Parameters

  1. Segment(V_2, W_2) → j_2
  2. Point(j_2) → D_3
  3. Point(j_2) → C_3
  4. Point(j_2) → Z_2
  5. CountIf(x > 0, B27:B29) → B31
  6. Segment(E, F) → c
  7. Point(c) → T
  8. Point(c) → S
  9. Point(c) → R
  10. Point(c) → Q
  11. Segment(C, D) → b
  12. Point(b) → P
  13. Point(b) → N
  14. Point(b) → M
  15. Point(b) → L
  16. CountIf(x < 0, B17:B20) → B24
  17. Segment(A, B) → a
  18. Point(a) → K
  19. Point(a) → J
  20. Point(a) → I
  21. Point(a) → O
  22. CountIf(x > 0, B1:B8) → B14
  23. Segment(Q_3, R_3) → k_2
  24. Point(k_2) → T_3
  25. Point(k_2) → S_3
  26. CountIf(x > 0, A28:A29) → A32
  27. Segment(A_1, B_1) → i
  28. Point(i) → E_1
  29. CountIf(x > 0, A13:A13) → A14
  30. Point(i) → D_1
  31. Point(i) → C_1
  32. CountIf(x > 0, A7:A8) → A10
  33. Segment(G, H) → d
  34. Point(d) → Z
  35. Point(d) → W
  36. Point(d) → V
  37. Point(d) → U
  38. CountIf(x > 0, A19:A22) → A25
  39. Segment(A_2, B_2) → a_1
  40. Circle(Q, 0.5) → e
  41. Circle(R, 0.5) → f
  42. Circle(S, 0.5) → g
  43. Circle(T, 0.5) → h
  44. Circle(I, 0.5) → k
  45. Circle(J, 0.5) → p
  46. Circle(K, 0.5) → q
  47. Circle(O, 0.5) → r
  48. Circle(U, 0.5) → s
  49. Circle(V, 0.5) → t
  50. Circle(W, 0.5) → c_1
  51. Circle(Z, 0.5) → d_1
  52. Segment(F_1, G_1) → j
  53. OrthogonalLine(C_1, i) → l
  54. OrthogonalLine(D_1, i) → m
  55. OrthogonalLine(E_1, i) → n
  56. Point(Circle[C_1, 2.000099997500125]) → H_1
  57. Polygon(C_1, H_1, I_1, J_1) → poly1, c_2, h_1, i_1, j_1
  58. Point(Circle[D_1, 2]) → K_1
  59. Polygon(D_1, K_1, L_1, M_1) → poly2, d_2, k_1, l_1, m_1
  60. Point(a_1) → J_2
  61. Point(a_1) → K_2
  62. Point(a_1) → O_1
  63. Segment(A_3, B_3) → a_2
  64. Point(a_2) → I_3
  65. Point(a_2) → K_3
  66. Point(a_2) → O_2
  67. Segment(A_4, B_4) → a_3
  68. Point(a_3) → I_4
  69. Point(a_3) → J_4
  70. Point(a_3) → O_3
  71. Point(Circle[L, 0.8280096617793782]) → N_1
  72. Polygon(L, N_1, P_1) → poly3, p_1, l_2, n_1
  73. Point(Circle[M, 0.7161005515987262]) → Q_1
  74. Polygon(M, Q_1, R_1) → poly4, r_1, m_2, q_1
  75. Point(Circle[N, 0.6997142273814358]) → S_1
  76. Polygon(N, S_1, T_1) → poly5, t_1, n_2, s_1
  77. Point(Circle[P, 0.7211102550927978]) → U_1
  78. Polygon(P, U_1, V_1) → poly6, v_1, p_2, u_1
  79. Point(xAxis) → W_1
  80. Point(xAxis) → D_2
  81. Polygon(W_1, Z_1, C_2, D_2) → poly7, w_1, z_1, c_3, d_3
  82. Point(Circle[E_1, 2.0502987587178603]) → E_2
  83. Polygon(E_1, E_2, F_2, G_2) → poly8, e_1, e_2, f_2, g_2
  84. Point(yAxis) → H_2
  85. Point(d_3) → I_2
  86. Point(yAxis) → L_2
  87. Point(d_3) → M_2
  88. Segment(L_2, M_2) → b_1
  89. Point(d_3) → N_2
  90. Segment(L_2, N_2) → f_1
  91. Segment(M_2, N_2) → g_1
  92. Polygon(L_2, M_2, N_2) → poly9, n_3, l_3, m_3
  93. Segment(P_2, Q_2) → b_2
  94. Segment(R_2, S_2) → h_2
  95. Sum(C3:C6) → C8
  96. CountIf(x > 0, C12:C12) → C13
  97. CountIf(x > 0, D12:D12) → D13
  98. Segment(T_2, U_2) → i_2
  99. Point(Circle[Z_2, 1.8080613758656188]) → E_3
  100. Polygon(Z_2, E_3, F_3, G_3) → poly10, z_2, e_3, f_3, g_3
  101. Point(Circle[C_3, 1.697060394712511]) → H_3
  102. Polygon(C_3, H_3, J_3, L_3) → poly11, c_4, h_3, j_3, l_4
  103. Point(Circle[D_3, 1.765030632264185]) → M_3
  104. Polygon(D_3, M_3, N_3, P_3) → poly12, d_4, m_4, n_4, p_3
  105. Point(Circle[S_3, 0.7572989883260863]) → U_3
  106. Polygon(S_3, U_3, V_3) → poly13, v_3, s_3, u_3
  107. Point(Circle[T_3, 0.7697908875840829]) → W_3
  108. Polygon(T_3, W_3, Z_3) → poly14, z_3, t_3, w_3
  109. Point(f_1) → C_4
  110. Point(d_3) → D_4
  111. Polygon(C_4, D_4, 3) → poly15, q_2, r_2, s_2, E_4

AI Drawing Prompt Reference

Draw a geometric figure for inequality balancing, including two line segments j and c, and their four points D, C, Z, T, S, R, Q, P, N, M, L. Use CountIf to count positive and negative numbers. Draw four circles centered at T, S, R, Q with a radius of 0.5.
The prompt above was compiled from the original drawing commands and is for reference only.