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向量与线性函数的交互演示

向量与线性函数的交互演示
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2019-02-13 21:18
向量函数解析几何几何作图
①本范例演示了向量、线性函数与几何图形的交互关系，通过动态构造展示斜率、距离和旋转效果；②涉及的核心数学概念包括向量运算、线性函数、斜率计算、几何变换和距离公式；③作图要点提炼自构造摘要，使用了Line（直线）、Point（点）、Ray（射线）、Circle（圆）、Intersect（交点）、Segment（线段）、Distance（距离）、If（条件判断）、Zip（组合）、Rotate（旋转）等GeoGebra命令和对象；④适合高中数学教学，用于帮助学生理解向量、函数与几何的关联，提升空间想象和动态几何分析能力。

GeoGebra 命令及参数

  1. Line(A, xAxis) → a
  2. Point(a) → B
  3. Ray(A, B) → e
  4. Point(e) → C
  5. Circle(A, C) → d
  6. Intersect(d, a, 1) → D
  7. Segment(D, C) → f
  8. Distance(A, C) → AC
  9. If(Ms ≟ "", Sequence[(p, y(A) + 0.2), p, x(A) + OneDiv10, x(A) + AC - OneDiv10, OneDiv10], Sequence[(q, y(A) + 0.2), q, x(A) - OneDiv10, x(A) - AC + OneDiv10, 0 - OneDiv10]) → ListTop
  10. If(Ms ≟ "", Sequence[(p, y(A) - 0.2), p, x(A) + OneDiv10, x(A) + AC - OneDiv10, OneDiv10], Sequence[(q, y(A) - 0.2), q, x(A) - OneDiv10, x(A) - AC + OneDiv10, 0 - OneDiv10]) → ListBottom
  11. Zip(Segment[p, q], p, ListTop, q, ListBottom) → ScaleSeg
  12. If(Ms ≟ "", (x(A) + (b * OneDiv10) + (c * OneDiv100), y(A)), (x(A) - (b * OneDiv10) - (c * OneDiv100), y(A))) → E
  13. If(Ms ≟ "", Sequence[(p, y(A) - 0.15), p, x(A) + (b * OneDiv10) + OneDiv100, x(A) + ((b + 1) * OneDiv10) - OneDiv100, OneDiv100], Sequence[(q, y(A) - 0.15), q, x(A) - (b * OneDiv10) - OneDiv100, x(A) - ((b + 1) * OneDiv10) + OneDiv100, 0 - OneDiv100]) → ListBottomS
  14. If(Ms ≟ "", Sequence[(p, y(A) + 0.15), p, x(A) + (b * OneDiv10) + OneDiv100, x(A) + ((b + 1) * OneDiv10) - OneDiv100, OneDiv100], Sequence[(q, y(A) + 0.15), q, x(A) - (b * OneDiv10) - OneDiv100, x(A) - ((b + 1) * OneDiv10) + OneDiv100, 0 - OneDiv100]) → ListTopS
  15. Zip(Segment[p, q], p, ListTopS, q, ListBottomS) → ScaleSegS
  16. Segment((x(E), y(E) + 0.4), (x(E), y(E) - 0.4)) → g
  17. Circle(C, 1) → k
  18. Intersect(k, a, 2) → F
  19. Circle(F, 0.4) → p
  20. Intersect(p, a, 1) → G
  21. Rotate(G, 30°, F) → G'
  22. Rotate(G, (-(30°)), F) → G'_1
  23. Segment(F, G'_1) → j
  24. Segment(F, G') → l
  25. Segment(C, F) → m
  26. Circle(D, 1) → q
  27. Intersect(q, a, 1) → H
  28. Circle(H, 0.4) → r
  29. Intersect(r, a, 2) → I
  30. Rotate(I, 30°, H) → I'
  31. Rotate(I, (-(30°)), H) → I'_1
  32. Segment(I'_1, H) → n
  33. Segment(H, I') → s
  34. Segment(H, D) → t