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描述图形的反射

描述图形的反射
几何画板及绘图内容加载中，请稍等……
2023-02-20 12:14
解析几何变换几何作图
本范例演示如何在坐标系中绘制图形的反射。涉及的核心数学概念是图形关于直线的反射。作图要点——从下方『构造摘要』提炼用到了哪些 GeoGebra 命令/对象：Shuffle, Element, If, Mod, Vector, Translate, LineBisector, Rotate, Mirror, Polygon, Corner, Segment, Zip, Point, Line, IntersectPath, Intersect, Text, circlePixels；适合的学段或用途：6-8年级，用于学习如何描述图形的反射。

GeoGebra 命令及参数

  1. Shuffle(Sequence[40]) → randomList2, {26, 2, 34, 40, 35, 12, 22, 25, 5, 4, 3, 19, 15, 37, 30, 7, 24, 14, 1, 16, 8, 17, 33, 11, 32, 9, 38, 31, 18, 10, 39, 13, 36, 27, 23, 21, 20, 6, 28, 29}
  2. Element(randomList2, Mod[countQuestion, 40] + 1) → randomNum2
  3. Shuffle(Sequence[20]) → randomList1, {15, 3, 5, 19, 1, 20, 12, 17, 11, 13, 14, 10, 8, 9, 6, 4, 18, 2, 16, 7}
  4. Shuffle(Sequence[15]) → randomList3, {5, 13, 9, 3, 12, 10, 7, 1, 2, 4, 15, 6, 11, 8, 14}
  5. Element(randomList3, Mod[countQuestion, 15] + 1) → randomNum3
  6. Element(listYCoordInitCenter, Mod[randomNum3, Length[listYCoordInitCenter]] + 1) → yInitCenter
  7. Shuffle(Sequence[15]) → randomList5, {15, 9, 10, 6, 7, 11, 8, 1, 14, 3, 12, 13, 5, 4, 2}
  8. Element(randomList5, Mod[countQuestion, 15] + 1) → randomNum5
  9. If(Mod[randomNum1, 2] ≟ 1, yInitCenter, Element[listYCoordImgCenter, Mod[randomNum5, Length[listYCoordImgCenter]] + 1]) → yInitCenterImg
  10. Element(listXCoordInitCenter, Mod[randomNum2, Length[listXCoordInitCenter]] + 1) → xInitCenter
  11. Shuffle(Sequence[15]) → randomList4, {7, 12, 15, 2, 10, 1, 6, 8, 11, 9, 14, 3, 4, 13, 5}
  12. Element(randomList4, Mod[countQuestion, 15] + 1) → randomNum4
  13. If(Mod[randomNum1, 2] ≟ 0, xInitCenter, Element[listXCoordImgCenter, Mod[randomNum4, Length[listXCoordImgCenter]] + 1]) → xInitCenterImg
  14. Shuffle(Sequence[15]) → randomList6, {4, 7, 14, 8, 1, 12, 5, 9, 2, 3, 10, 6, 15, 11, 13}
  15. Mod(Element[randomList6, Mod[countQuestion, 15] + 1], 4) → randomNum6
  16. Vector(CenterPoint, (xInitCenter, yInitCenter)) → vectorInitial
  17. Translate(CenterPoint, vectorInitial) → CenterPointPre
  18. LineBisector(CenterPointPre, CenterPointImg) → lineReflection
  19. Rotate(Translate[listBasicVertices(randomNum1), vectorInitial], (90° * randomNum6), CenterPointPre) → verticesPre
  20. Mirror(verticesPre, lineReflection) → verticesImg
  21. Shuffle(Sequence[15]) → randomList7, {5, 4, 9, 1, 12, 3, 11, 6, 10, 8, 13, 2, 14, 15, 7}
  22. Polygon(Zip[PixelsToPoint[Corner[1], Corner[3], Corner[5], A], A, {(pixelsLeft, pixelsTop), (pixelsLeft, y(Corner[5]) - pixelsBottom), Corner[5] - (pixelsRight, pixelsBottom), (x(Corner[5]) - pixelsRight, pixelsTop)}]) → borderBox
  23. Corner(5) → layoutAppSize
  24. Polygon({(16, 9), (-16, 9), (-16, -9), (16, -9)}) → viewBox
  25. Segment((-15.9, 0), (15.9, 0)) → axisX
  26. Segment((0, -8.9), (0, 8.9)) → axisY
  27. Polygon(verticesPre) → FigurePre
  28. Polygon(verticesImg) → FigureImg
  29. Zip(FromTo[AA, BB, timer], AA, verticesPre, BB, verticesImg) → verticesSt
  30. Polygon(verticesSt) → FigureSt
  31. Point(Sequence[Sequence[(a, b), a, -8, 8], b, -8, 8]) → Input1
  32. Point(Sequence[Sequence[(a, b), a, -8, 8], b, -8, 8]) → Input2
  33. Line(Input1, Input2) → lineReflectionStAux
  34. Zip(Segment[AA, BB], AA, verticesPre, BB, verticesSt) → dashedSegments
  35. IntersectPath(lineReflectionStAux, viewBox) → lineReflectionSt
  36. IntersectPath(lineReflection, viewBox) → lineReflectionArrows
  37. Intersect(Circle[CenterPointPre, Distance[CenterPointPre, A] + 0.7], Ray[CenterPointPre, A]) → posLblPointPre,
  38. Mirror(posLblPointPre, lineReflection) → posLblPointImg
  39. Text("A^\prime", posLblPointImg, false, true, 0, 0) → lblA'
  40. Text("A", posLblPointPre, false, true, 0, 0) → lblA
  41. circlePixels(Input2, 7 + (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingObject

AI 绘图提示语参考

绘制一个图形及其关于某直线的反射图形。首先，确定原图形的顶点，然后通过旋转和平移找到反射顶点，接着画出原图形和反射图形。最后，画出连接原顶点和反射顶点的线段，并标出原顶点和反射顶点。
以上提示语为根据原始绘图命令整理而来，仅供参考。