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绘制相似矩形

绘制相似矩形
几何画板及绘图内容加载中，请稍等……
2018-03-02 22:24
多边形解析几何几何作图
①本范例演示如何通过 GeoGebra 绘制相似矩形；②涉及的核心数学概念包括矩形、相似图形、比例、特殊点；③作图要点：使用了 Join, Point, Sort, Polygon, If, Circle, Ray, Rotate, Angle, Segment, Random, LaTeX, Line 等命令和对象；④适合初中及以上学生学习和探索相似图形的性质。

GeoGebra 命令及参数

  1. Join({Sequence[Sequence[(i, j), i, -10, 10, 1], j, -10, 10, 1], {(15, 6.5), (16.5, 6.5), (18, 6.5), (19.5, 6.5)}}) → GridSpace
  2. Point(GridSpace) → A1
  3. Point(GridSpace) → B1
  4. Point(GridSpace) → C1
  5. Point(GridSpace) → D1
  6. Sort({A1, B1, C1, D1}) → ListX
  7. Polygon((10.5, 9), (25, 9), (25, -10), (10.5, -10)) → RightBox, j, k, l, m
  8. Polygon((14, 7.2), (14, 5.8), (20.5, 5.8), (20.5, 7.2)) → PointsBox, n, p, q, r
  9. Polygon((-12, 7.4), (25, 7.4), (25, 15), (-12, 15)) → TopBox, f, g, h, i
  10. If(y(Element[ListX, 1]) ≥ y(Element[ListX, 2]) ∧ y(Element[ListX, 3]) ≥ y(Element[ListX, 4]) ∨ y(Element[ListX, 1]) ≤ y(Element[ListX, 2]) ∧ y(Element[ListX, 3]) ≤ y(Element[ListX, 4]), Polygon[Element[ListX, 2], Element[ListX, 1], Element[ListX, 3], Element[ListX, 4]], Polygon[Element[ListX, 1], Element[ListX, 2], Element[ListX, 3], Element[ListX, 4]]) → ABC1
  11. Polygon(Acorr, Bcorr, Ccorr, Dcorr) → ABCcorr, i_1, j_1, k_1, l_1
  12. Circle((0, 0), 7) → Circ1
  13. Point(Circ1) → RotPt
  14. Ray(C, RotPt) → s
  15. Rotate(RotPt, (angledisp * π / 180)) → RotPtb
  16. Ray(C, RotPtb) → t
  17. Angle(RotPtb, C, RotPt) → HelpAngle
  18. Segment((0, 7.3), (0, -8)) → yaxis
  19. Random(2, 4) → ScaleFactor
  20. LaTeX("Draw\ a\ rectangle\ that\ is\ similar\ to\ ABCD\ by\ a\ scale\ factor\ of\ " + ScaleFactor + "\ using\ the\ method\ described\\ in\ the\ previous\ example.") → Instructions1
  21. Random(1, 3) → HorizontalLength
  22. Random(1, 2) → VerticalLength
  23. Polygon(A, B, C, D) → q1, a, b, c, d
  24. Line(A, C) → DiagL1
  25. Line(D, B) → DiagL2
  26. LaTeX("\textbf{Instructions\text{:}}\ Drag\ the\ points\ onto\ the\ grid\ to\ draw\ the\ similar\ quadrilateral.") → Instructions2
  27. LaTeX("The\ quadrilateral\ you\\ have\ drawn\ is\ similar\ to\\ ABCD\ but\ not\ by\ a\\ scale\ factor\ of\ " + ScaleFactor + ".\\ Use\ the\ grid\ to\ place\ the\\ points\ " + ScaleFactor + "\ times\ as\ far\ from\\ O\ as\ A\ B\ C,\, and\ D.") → FBSimilar
  28. Sort({A, B, C, D}) → SortedQuadList