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线段中点的探索（LR7-01-XT1）

线段中点的探索（LR7-01-XT1）
几何画板及绘图内容加载中，请稍等……
2019-05-09 01:41
解析几何几何作图滑块动画
本范例通过交互式几何画板演示线段中点的确定方法，直观展示中点将线段平分为两等份的几何性质。核心数学概念包括线段、中点、长度测量以及坐标表示。作图要点方面，构造中使用了Polygon、Segment、Midpoint、Length、Point、Angle、Rotate、Line、Vector等GeoGebra命令，并设计了多个滑块（如sliderDrawFirstHalfSegment、sliderDrawSecondHalfSegment、sliderXFirstHalf等）来控制线段的分段显示与动态移动，同时利用LaTeX文本和坐标点（xCoordinate、yCoordinate）辅助说明。该范例适合初中或高中阶段学习平面几何与解析几何的学生，可用于课堂演示或自主探究，帮助理解中点公式及其在坐标系中的应用。

GeoGebra 命令及参数

  1. Polygon({(-6, -1), (-3, -1), (-3, -9), (-6, -9)}) → pointABox
  2. Polygon({(7, 10), (3, 10), (3, 1), (7, 1)}) → pointBBox
  3. Polygon({(-11, -11), (-11, 11), (11, 11), (11, -11)}) → viewBox
  4. LaTeX((((("\text{" * QUESTION) * "\\") * INSTRUCTIONS) * "}")) → TEXT
  5. PointIn(pointABox) → A
  6. PointIn(pointBBox) → B
  7. Segment(A, B) → segment
  8. Midpoint(segment) → midpoint
  9. Length(Segment[A, midpoint]) → lengthOfHalfSegment
  10. Point(Circle[A, sliderDrawFirstHalfSegment]) → C
  11. Angle(C, A, midpoint) → α
  12. Rotate(Segment[A, Point[Circle[A, sliderDrawFirstHalfSegment]]], α, A) → firstHalfSegment
  13. Rotate(firstHalfSegment, sliderDrawSecondHalfSegment°, midpoint) → secondHalfSegment
  14. Line(A, x = 0) → xLineA
  15. Line(B, x = 0) → xLineB
  16. Segment(D, E) → segmentX
  17. Midpoint(segmentX) → midpointX
  18. Length(Segment[D, midpointX]) → lengthOfHalfX
  19. Point(Circle[D, sliderXFirstHalf]) → F
  20. Segment(D, F) → firstHalfX
  21. Rotate(D, sliderXSecondHalf°, midpointX) → D'
  22. Rotate(F, sliderXSecondHalf°, midpointX) → F'
  23. Segment(D', F') → secondHalfX
  24. Vector(D + (0, (-sliderXMove)), D + (0, (-sliderXMove)) + (sliderXArrows, 0)) → x1Vector
  25. Vector(E + (0, (-sliderXMove)), E + (0, (-sliderXMove)) + ((-sliderXArrows), 0)) → x2Vector
  26. LaTeX("\text{\(x\)-coordinate}") → xLabel
  27. LaTeX("\text{\(y\)-coordinate}") → yLabel
  28. Line(A, y = 0) → yLineA
  29. Line(B, y = 0) → yLineB
  30. LaTeX(("x=" * x(A))) → xLineALabel
  31. LaTeX(("\vphantom{-}x=" * x(B))) → xLineBLabel
  32. LaTeX(("y=" * y(A))) → yLineALabel
  33. LaTeX(("y=" * y(B))) → yLineBLabel
  34. Segment(G, H) → segmentY
  35. Point(Circle[G, sliderYFirstHalf]) → I
  36. Midpoint(segmentY) → midpointY
  37. Length(Segment[G, midpointY]) → lengthOfHalfY
  38. Rotate(Segment[G, Point[Circle[G, sliderYFirstHalf]]], 90°, G) → firstHalfY
  39. Rotate(firstHalfY, sliderYSecondHalf°, midpointY) → secondHalfY
  40. LaTeX((((("\text{The \(y\)-coordinate of the midpoint is halfway between the lines \(" * yLineALabel) * "\) and \(") * yLineBLabel) * "\).}")) → ySummary
  41. LaTeX((((("\text{The \(x\)-coordinate of the midpoint is halfway between the lines \(" * xLineALabel) * "\) and \(") * xLineBLabel) * "\).}")) → xSummary
  42. Vector(G + ((-sliderYMove), 0), G + ((-sliderYMove), 0) + (0, sliderYArrows)) → y1Vector
  43. Vector(H + ((-sliderYMove), 0), H + ((-sliderYMove), 0) + (0, (-sliderYArrows))) → y2Vector
  44. LaTeX(("A" * A)) → aLabel
  45. LaTeX(("B" * B)) → bLabel