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描述图形的水平与垂直平移

描述图形的水平与垂直平移
几何画板及绘图内容加载中，请稍等……
2023-02-13 21:35
向量解析几何变换几何作图
本范例演示如何在坐标系中水平与垂直平移图形。涉及的核心数学概念包括平移变换、坐标变换。作图要点——从下方『构造摘要』提炼用到了哪些 GeoGebra 命令/对象：Shuffle, Vector, Mod, Element, Translate, Rotate, Textfield, Polygon, Corner, Segment, Intersect, Text；对象：input2, listBasicVertices, randomList6, input1, vectorSt, listCenters, countQuestion, randomNum6, randomList2, randomNum2, randomList1, randomNum1, CenterPoint, radios, radiusFig, listCoordInitCenter, xInitCenter, randomList3, randomNum3, yInitCenter, vectorInitial, CenterPointPre, verticesPre, randomList4, randomNum4, yInitCenterImg, xInitCenterImg, CenterPointImg, xMax, yMin, randomList7, vectorTransl, randomList5, randomNum5, colorGreyDark, btnNew, InputBox1, correct, scriptResetApp, colorTealSuccess。适合的学段或用途：6-8年级，学习如何描述图形的平移变换。

GeoGebra 命令及参数

  1. Shuffle(Sequence[15]) → randomList6, {1, 3, 14, 9, 7, 6, 15, 8, 4, 13, 10, 12, 5, 2, 11}
  2. Vector((input1, input2)) → vectorSt
  3. Mod(Element[randomList6, Mod[countQuestion, 15] + 1], 4) → randomNum6
  4. Shuffle(Sequence[15]) → randomList2, {3, 2, 14, 12, 7, 15, 6, 8, 4, 10, 9, 5, 13, 1, 11}
  5. Element(randomList2, Mod[countQuestion, 15] + 1) → randomNum2
  6. Shuffle(Sequence[20]) → randomList1, {4, 8, 14, 6, 9, 13, 2, 3, 1, 20, 17, 5, 15, 16, 10, 7, 11, 18, 12, 19}
  7. Element(listCoordInitCenter, Mod[randomNum2, Length[listCoordInitCenter]] + 1) → xInitCenter
  8. Shuffle(Sequence[15]) → randomList3, {15, 5, 2, 7, 12, 14, 3, 1, 4, 13, 11, 10, 8, 6, 9}
  9. Element(randomList3, Mod[countQuestion, 15] + 1) → randomNum3
  10. Element(listCoordInitCenter, Mod[randomNum3, Length[listCoordInitCenter]] + 1) → yInitCenter
  11. Vector(CenterPoint, (xInitCenter, yInitCenter)) → vectorInitial
  12. Translate(CenterPoint, vectorInitial) → CenterPointPre
  13. Rotate(Translate[listBasicVertices(randomNum1), vectorInitial], (90° * randomNum6), CenterPointPre) → verticesPre
  14. Shuffle(Sequence[15]) → randomList4, {7, 5, 4, 6, 3, 9, 14, 13, 2, 11, 15, 12, 8, 1, 10}
  15. Element(randomList4, Mod[countQuestion, 15] + 1) → randomNum4
  16. Element(listCoordInitCenter \ Sequence[yInitCenter - 2, yInitCenter + 2], Mod[randomNum4, Length[listCoordInitCenter \ Sequence[yInitCenter - 2, yInitCenter + 2]]] + 1) → yInitCenterImg
  17. Element(listCoordInitCenter \ Sequence[xInitCenter - 2, xInitCenter + 2], Mod[randomNum4, Length[listCoordInitCenter \ Sequence[xInitCenter - 2, xInitCenter + 2]]] + 1) → xInitCenterImg
  18. Shuffle(Sequence[15]) → randomList7, {10, 4, 1, 8, 14, 6, 5, 3, 11, 2, 13, 9, 12, 15, 7}
  19. Vector(CenterPointPre, CenterPointImg) → vectorTransl
  20. Shuffle(Sequence[15]) → randomList5, {4, 2, 15, 7, 12, 14, 13, 6, 10, 11, 9, 8, 5, 3, 1}
  21. Element(randomList5, Mod[countQuestion, 15] + 1) → randomNum5
  22. Textfield(input1) → InputBox1
  23. 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
  24. Corner(5) → layoutAppSize
  25. Polygon({(9, 9), (-9, 9), (-9, -9), (9, -9)}) → viewBox
  26. Segment((-9, 0), (9, 0)) → axisX
  27. Segment((0, -9), (0, 9)) → axisY
  28. Polygon(verticesPre) → FigurePre
  29. Translate(verticesPre, vectorTransl) → verticesImg
  30. Polygon(verticesImg) → FigureImg
  31. Translate(verticesPre, vectorSt) → verticesSt
  32. Polygon(verticesSt) → FigureSt
  33. Intersect(Circle[CenterPointPre, Distance[CenterPointPre, A] + 0.8], Ray[CenterPointPre, A]) → posLblPointPre,
  34. Translate(posLblPointPre, vectorTransl) → posLblPointImg
  35. Text("A", posLblPointPre, false, true, 0, 0) → lblA
  36. Text("A^\prime", posLblPointImg, false, true, 0, 0) → lblA'

AI 绘图提示语参考

在直角坐标系中画一张初始平面图形，并在其上建立一个“刚体运动”的对照过程：先给定一组顶点形成多边形作为原图，标出坐标轴与画面边界视窗。再选取初始平移向量，把原图平移得到第一张图像。接着以旋转后的顶点集合为基础，再根据另一条由原图到目标位置的平移向量，构造第二次平移得到目标图像。最后在两次对应位置附近放置标记点，并写出点的符号标注为 A 与 A′，用以对应展示从原位置到移动后位置的关系。
以上提示语为根据原始绘图命令整理而来，仅供参考。