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坐标平面上的三角形旋转

坐标平面上的三角形旋转
几何画板及绘图内容加载中，请稍等……
2023-01-10 11:22
测试改名0解析几何变换几何作图
本范例演示了在坐标平面上对三角形进行旋转的操作。通过动画展示不同方向、角度和旋转中心的三角形旋转效果。涉及的核心数学概念包括旋转、坐标变换和几何变换。作图要点使用了GeoGebra命令如Rotate、UnitOrthogonalVector、Angle等来构建旋转动画和轨迹。适合6-8年级学生学习解析几何和几何变换。

GeoGebra 命令及参数

  1. Shuffle(Sequence[100]) → randomList2, {41, 64, 98, 6, 11, 34, 90, 18, 29, 82, 72, 21, 88, 52, 36, 86, 10, 33, 22, 62, 89, 32, 26, 37, 73, 74, 27, 15, 80, 65, 95, 45, 99, 13, 50, 58, 91, 44, 1, 51, 2, 16, 47, 79, 9, 60, 55, 85, 78, 25, 48, 43, 92, 38, 28, 19, 69, 87, 57, 35, 49, 30, 97, 20, 75, 70, 42, 68, 46, 61, 24, 81, 39, 100, 76, 7, 4, 59, 54, 83, 5, 8, 77, 93, 14, 12, 56, 67, 40, 53, 71, 3, 23, 66, 17, 96, 94, 31, 63, 84}
  2. Shuffle(Sequence[100]) → randomList1, {54, 48, 30, 63, 96, 57, 84, 51, 15, 2, 92, 10, 45, 77, 68, 100, 72, 87, 7, 55, 80, 37, 22, 56, 4, 67, 61, 62, 60, 89, 32, 43, 58, 12, 71, 38, 31, 65, 70, 49, 66, 1, 11, 3, 53, 9, 46, 36, 23, 28, 79, 18, 52, 35, 25, 99, 14, 78, 6, 19, 16, 93, 97, 39, 59, 24, 90, 21, 20, 91, 69, 94, 5, 26, 64, 73, 85, 82, 95, 40, 8, 13, 86, 76, 34, 88, 98, 41, 81, 50, 75, 17, 27, 83, 29, 47, 42, 44, 33, 74}
  3. Zip((("$\text{" * A) * "}$"), A, {"90^\circ ", "180^\circ", "270^\circ"}) → selectAngle
  4. SelectedIndex(selectAngle) → selectedAngle
  5. Zip((("$\text{" * A) * " }$"), A, {"clockwise", "counterclockwise"}) → selectDirection
  6. SelectedIndex(selectDirection) → selectedDirection
  7. Flatten(Sequence[Sequence[(i, j), i, -10, 10], j, -10, 10]) → gridPoints
  8. Element(randomList1, Mod[countQuestion, Length[randomList1]] + 1) → randomNum1
  9. Element({verticesCase1(indexCase1), verticesCase2(indexCase2), verticesCase3(indexCase3)}, caseNum) → currentVertices
  10. ClosestPoint(gridPoints, TriangleCenter[currentVertices(1), currentVertices(2), currentVertices(3), 1]) → CenterCase2
  11. Element({(0, 0), CenterCase2, centersCase3(indexCase3)}, caseNum) → RotationPoint
  12. Element(randomList2, Mod[countQuestion, Length[randomList2]] + 1) → randomNum2
  13. Corner(5) → layoutAppSize
  14. Polygon({(-10.5, -10.5), (-10.5, 10.5), (10.5, 10.5), (10.5, -10.5)}) → viewbox
  15. Zip(Vector[UnitVector[Vector[CenterCase2, A]]], A, currentVertices) → vLabels
  16. Polygon(currentVertices) → triABC
  17. Rotate(triABC, (slideRotate * rotateAngle°), RotationPoint) → rotationTriangle
  18. Zip(Distance[RotationPoint, A], A, currentVertices) → distanceToCenter
  19. IndexOf(Max[distanceToCenter], distanceToCenter) → whichIndex
  20. Sequence(Vertex[rotationTriangle, A], A, 1, 3) → rotatedVertices
  21. Zip(Vector[Rotate[A, rotateDegrees°, RotationPoint]], Vector[A], vLabels) → vLabelsRotated
  22. Angle(currentVertices(whichIndex), RotationPoint, rotatedVertices(whichIndex)) → showAngleCounterClockwise
  23. Angle(rotatedVertices(whichIndex), RotationPoint, currentVertices(whichIndex)) → showAngleClockwise
  24. UnitOrthogonalVector(Segment[RotationPoint, rotatedVertices(whichIndex)]) → vArrow
  25. Zip(Text[("" * A), B + C, false, true, 0, 0], A, {"A", "B", "C"}, B, currentVertices, Vector[C], vLabels) → labelsABC
  26. Zip(Text[("" * A), B + C, false, true, 0, 0], A, {"A^{\prime}", "B^{\prime}", "C^{\prime}"}, B, rotatedVertices, Vector[C], vLabelsRotated) → labelsABCPrime
  27. CircleArc(RotationPoint, If[¬clockwiseDirection, currentVertices(whichIndex), rotatedVertices(whichIndex)], If[¬clockwiseDirection, rotatedVertices(whichIndex), currentVertices(whichIndex)]) → displayRotation
  28. Segment(rotatedVertices(whichIndex) + (If[¬clockwiseDirection, -1, 1] * vArrow), rotatedVertices(whichIndex)) → directionArrow
  29. Segment((-10.5, 0), (10.5, 0)) → axisSegmentX
  30. Segment((0, -10.5), (0, 10.5)) → axisSegmentY
  31. Text("y", (0, 11), true, true, 0, 0) → lblY
  32. Text("x", (11.3, 0), true, true, 0, 0) → lblX

AI 绘图提示语参考

在坐标平面上绘制一个三角形，并展示其旋转动画。图形包含一个初始三角形、旋转后的三角形、旋转中心、角度指示和方向箭头。构造顺序为：先绘制坐标平面和网格，然后放置初始三角形，确定旋转中心，接着旋转三角形并显示旋转角度和方向，最后添加标签和箭头以说明旋转过程。
以上提示语为根据原始绘图命令整理而来，仅供参考。