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解线性方程：分组符号与分数处理

解线性方程：分组符号与分数处理
几何画板及绘图内容加载中，请稍等……
2012-09-29 15:00
向量函数解析几何几何作图函数图像
这个GeoGebra范例演示了如何在几何图形环境中求解线性方程，重点涉及分组符号（如括号）和分数运算。核心数学概念包括线性方程的求解步骤、分数简化、字面方程中变量的隔离以及代数表达式的处理。作图要点：从构造摘要可见，使用了Polygon命令绘制多边形作为背景图形，Segment命令绘制线段辅助标注，If命令实现条件逻辑控制步骤显示，PointIn命令检查点是否在图形内以交互验证，Point和Vector命令处理坐标点和方向向量，Sequence命令生成序列化步骤。对象如row4Step3、solveHead等用于构建逐步求解界面，适合初中或高中数学教育，用于方程求解的教学与练习。

GeoGebra 命令及参数

  1. Polygon((0, -1.5), (4, -1.5), (4, 3), (0, 3)) → row4Step3, i, j, k, l
  2. Polygon((-1.5, 0), (9.5, 0), (9.5, 6), (-1.5, 6)) → row2Step1, e, f, g, b_3
  3. Polygon((0, 3), (4, 3), (4, 5), (0, 5)) → row3step2, m, n, p, q
  4. Polygon((4, -1.5), (9.5, -1.5), (9.5, 0), (4, 0)) → row2Check, r, s, checkBottomDivider, a_1
  5. Polygon((0, 6), (9.5, 6), (9.5, 7), (0, 7)) → row1Header, a_2, b, c, d
  6. Segment((x(Corner[solve2a_1, 1]), 2.1), (x(Corner[solve1_2, 2]), 2.1)) → step2segment
  7. If(b_4 - h ≟ 0 ∧ (a ≠ -constR) ∨ solution ≟ Infinity, true, false) → notValid
  8. Segment((4, 5), (4, 7)) → segmentDivider
  9. Segment((x(Corner[solve2a_1, 1]), 0), (x(Corner[solve1_2, 2]), 0)) → step3segment
  10. PointIn(Polygon[(5.5, 2), (10, 2), (10, 4), (5.5, 4)]) → E
  11. PointIn(Polygon[(5.5, 0.5), (10, 0.5), (10, 1.5), (5.5, 1.5)]) → B
  12. Point(Segment[B + (0.5, 0), (11, y(B))]) → C
  13. Point(Segment[E + (0.5, 0), (11, y(E))]) → D
  14. Segment(Midpoint[B, C], (x(Midpoint[B, C]), y(D))) → height
  15. Polygon(B, C, D, E) → trap, b_1, trapR, b_2, trapL
  16. Vector((If[x(C) > x(D), x(C), x(D)], y(C)) + (0.25, (y(D) - y(C)) / 2 + 0.1), (If[x(C) > x(D), x(C), x(D)], y(C)) + (0.25, 0)) → heightVectorBottom
  17. Vector((If[x(C) > x(D), x(C), x(D)], y(C)) + (0.25, (y(D) - y(C)) / 2 - 0.1), (If[x(C) > x(D), x(C), x(D)], y(D)) + (0.25, 0)) → heightVectorTop
  18. Segment((3.5, 5), (10.5, 5)) → checkTopDivider
  19. Sequence(Segment[(5.5 + i, 0), (5.5 + i, 5)], i, 0, 6, 0.5) → gridV
  20. Sequence(Segment[(5, 0.5 + i), (12, 0.5 + i)], i, 0, 4, 0.5) → gridH