积极 AI Logo 积极 AI

解二元线性不等式组

解二元线性不等式组
几何画板及绘图内容加载中，请稍等……
2016-05-24 07:29
解析几何不等式函数图像
本范例演示如何在二维坐标系中绘制并求解二元线性不等式组的解集。涉及的核心数学概念包括线性不等式、区域表示和边界直线。作图要点使用了GeoGebra的RandomElement, If, Simplify, Line等命令和对象来生成随机的不等式、绘制直线和显示解区域。适合高中数学学习和教学，用于理解不等式解集的几何意义。

GeoGebra 命令及参数

  1. RandomElement({1, 2, 3, 4}) → s4
  2. RandomElement({-4, -3, -2, -1, 1, 2, 3, 4}) → m3a
  3. RandomElement({1, 2, 3}) → m3b
  4. RandomElement({1, 2, 3} \ {m3b}) → m4b
  5. RandomElement({-4, -3, -2, -1, 0, 1, 2, 3, 4}) → x1
  6. RandomElement({1, 2, 3, 4}) → s1
  7. If(s1 ≟ 1, -1, 1) → k1
  8. RandomElement({x1 + k1, x1 + (k1 * 2), x1 + (k1 * 3), x1 + (k1 * 4)}) → x2
  9. RandomElement({-4, -3, -2, -1, 0, 1, 2, 3, 4}) → y1
  10. RandomElement({1, 2, 3, 4}) → s2
  11. If(s2 ≟ 1, -1, 1) → k2
  12. RandomElement({y1 + k2, y1 + (k2 * 2), y1 + (k2 * 3), y1 + (k2 * 4)}) → y2
  13. RandomElement({-4, -3, -2, -1, 1, 2, 3, 4}) → m4a
  14. If(s4 ≟ 1, (m4a * x) - (m4b * y) < (m4a * x2) - (m4b * y2), If[s4 ≟ 2, (m4a * x) - (m4b * y) ≤ (m4a * x2) - (m4b * y2), If[s4 ≟ 3, (m4a * x) - (m4b * y) > (m4a * x2) - (m4b * y2), (m4a * x) - (m4b * y) ≥ (m4a * x2) - (m4b * y2)]]) → h_1
  15. RandomElement({1, 2, 3, 4}) → s3
  16. If(s3 ≟ 1, (m3a * x) - (m3b * y) < (m3a * x2) - (m3b * y2), If[s3 ≟ 2, (m3a * x) - (m3b * y) ≤ (m3a * x2) - (m3b * y2), If[s3 ≟ 3, (m3a * x) - (m3b * y) > (m3a * x2) - (m3b * y2), (m3a * x) - (m3b * y) ≥ (m3a * x2) - (m3b * y2)]]) → g_1
  17. Simplify(g_1) → g
  18. Simplify(h_1) → h
  19. If(s1 ≟ 1, x < x1, If[s1 ≟ 2, x ≤ x1, If[s1 ≟ 3, x > x1, x ≥ x1]]) → e
  20. Line(A, B) → L1
  21. Line(C, D) → L2
  22. Line(E, F) → L3
  23. Line(G, H) → L4
  24. If(x(C) ≟ x(D), x > x(C), ((y - y(C)) * (x(C) - x(D))) - ((x - x(C)) * (y(C) - y(D))) > 0) → L2a
  25. If(x(C) ≟ x(D), x < x(C), ((y - y(C)) * (x(C) - x(D))) - ((x - x(C)) * (y(C) - y(D))) < 0) → L2b
  26. If(x(A) ≟ x(B), x > x(A), ((y - y(A)) * (x(A) - x(B))) - ((x - x(A)) * (y(A) - y(B))) > 0) → L1a
  27. If(x(A) ≟ x(B), x < x(A), ((y - y(A)) * (x(A) - x(B))) - ((x - x(A)) * (y(A) - y(B))) < 0) → L1b
  28. If(x(E) ≟ x(F), x > x(E), ((y - y(E)) * (x(E) - x(F))) - ((x - x(E)) * (y(E) - y(F))) > 0) → L3a
  29. If(x(E) ≟ x(F), x < x(E), ((y - y(E)) * (x(E) - x(F))) - ((x - x(E)) * (y(E) - y(F))) < 0) → L3b
  30. If(x(G) ≟ x(H), x > x(G), ((y - y(G)) * (x(G) - x(H))) - ((x - x(G)) * (y(G) - y(H))) > 0) → L4a
  31. If(x(G) ≟ x(H), x < x(G), ((y - y(G)) * (x(G) - x(H))) - ((x - x(G)) * (y(G) - y(H))) < 0) → L4b
  32. If(c1a ∧ c2a ∧ c3a ∧ c4a, L1a(x, y) ∧ L2a(x, y) ∧ L3a(x, y) ∧ L4a(x, y), If[c1a ∧ c2a ∧ c3a ∧ c4b, L1a(x, y) ∧ L2a(x, y) ∧ L3a(x, y) ∧ L4b(x, y), If[c1a ∧ c2a ∧ c3b ∧ c4a, L1a(x, y) ∧ L2a(x, y) ∧ L3b(x, y) ∧ L4a(x, y), If[c1a ∧ c2b ∧ c3a ∧ c4a, L1a(x, y) ∧ L2b(x, y) ∧ L3a(x, y) ∧ L4a(x, y), If[c1b ∧ c2a ∧ c3a ∧ c4a, L1b(x, y) ∧ L2a(x, y) ∧ L3a(x, y) ∧ L4a(x, y), If[c1b ∧ c2b ∧ c3a ∧ c4a, L1b(x, y) ∧ L2b(x, y) ∧ L3a(x, y) ∧ L4a(x, y), If[c1b ∧ c2a ∧ c3b ∧ c4a, L1b(x, y) ∧ L2a(x, y) ∧ L3b(x, y) ∧ L4a(x, y), If[c1b ∧ c2a ∧ c3a ∧ c4b, L1b(x, y) ∧ L2a(x, y) ∧ L3a(x, y) ∧ L4b(x, y), If[c1a ∧ c2b ∧ c3b ∧ c4a, L1a(x, y) ∧ L2b(x, y) ∧ L3b(x, y) ∧ L4a(x, y), If[c1a ∧ c2b ∧ c3a ∧ c4b, L1a(x, y) ∧ L2b(x, y) ∧ L3a(x, y) ∧ L4b(x, y), If[c1a ∧ c2a ∧ c3b ∧ c4b, L1a(x, y) ∧ L2a(x, y) ∧ L3b(x, y) ∧ L4b(x, y), If[c1b ∧ c2b ∧ c3b ∧ c4a, L1b(x, y) ∧ L2b(x, y) ∧ L3b(x, y) ∧ L4a(x, y), If[c1b ∧ c2b ∧ c3a ∧ c4b, L1b(x, y) ∧ L2b(x, y) ∧ L3a(x, y) ∧ L4b(x, y), If[c1b ∧ c2a ∧ c3b ∧ c4b, L1b(x, y) ∧ L2a(x, y) ∧ L3b(x, y) ∧ L4b(x, y), If[c1a ∧ c2b ∧ c3b ∧ c4b, L1a(x, y) ∧ L2b(x, y) ∧ L3b(x, y) ∧ L4b(x, y), If[c1b ∧ c2b ∧ c3b ∧ c4b, L1b(x, y) ∧ L2b(x, y) ∧ L3b(x, y) ∧ L4b(x, y)]]]]]]]]]]]]]]]) → checkSol
  33. Simplify((m3a * (x - x2)) + (y2 * m3b)) → g_2
  34. Simplify((m4a * (x - x2)) + (y2 * m4b)) → h_2
  35. If(s2 ≟ 1, (0 * x) + y < y1, If[s2 ≟ 2, (0 * x) + y ≤ y1, If[s2 ≟ 3, (0 * x) + y > y1, (0 * x) + y ≥ y1]]) → f_1
  36. Simplify(f_1) → f
  37. Line(A, B) → L1solid
  38. Line(C, D) → L2solid
  39. Line(E, F) → L3solid
  40. Line(G, H) → L4solid
  41. If(caly ≟ 3, y2 + (m3a / m3b * (tempx - x2)), If[caly ≟ 4, y2 + (m4a / m4b * (tempx - x2))]) → tempy