使用表格值画直线

使用表格值画直线
几何画板及绘图内容加载中,请稍等……
2020-11-21 20:30
本范例演示如何使用表格值绘制直线。核心数学概念包括解析几何中的直线方程。通过使用GeoGebra命令如Sequence、Point、Vector等,可以构造直线并理解其几何意义。适合初中及以上学生学习直线方程和解析几何。

GeoGebra 命令及参数

  1. Polygon((1.3, 0), (2.2, 0), 4) → poly2
  2. Polygon((1.3, 1), (2.2, 1), 4) → poly5
  3. Polygon((0, 0), (0.9, 0), 4) → poly1
  4. Polygon((0, 1), (0.9, 1), 4) → poly4
  5. Polygon((1.3, 2), (2.2, 2), 4) → poly8
  6. Polygon((0, 2), (0.9, 2), 4) → poly7
  7. Segment(J, K) → a
  8. If(IsInRegion[A, poly8], 1, If[IsInRegion[B, poly8], 2, If[IsInRegion[C, poly8], 3, If[IsInRegion[D, poly8], 4, If[IsInRegion[E, poly8], 5, If[IsInRegion[F, poly8], 6, If[IsInRegion[G, poly8], 7, If[IsInRegion[H, poly8], 8, If[IsInRegion[I, poly8], 9, 0]]]]]]]]) → y1
  9. If(IsInRegion[A, poly7], 1, If[IsInRegion[B, poly7], 2, If[IsInRegion[C, poly7], 3, If[IsInRegion[D, poly7], 4, If[IsInRegion[E, poly7], 5, If[IsInRegion[F, poly7], 6, If[IsInRegion[G, poly7], 7, If[IsInRegion[H, poly7], 8, If[IsInRegion[I, poly7], 9, 0]]]]]]]]) → x1
  10. If(IsInRegion[A, poly5], 1, If[IsInRegion[B, poly5], 2, If[IsInRegion[C, poly5], 3, If[IsInRegion[D, poly5], 4, If[IsInRegion[E, poly5], 5, If[IsInRegion[F, poly5], 6, If[IsInRegion[G, poly5], 7, If[IsInRegion[H, poly5], 8, If[IsInRegion[I, poly5], 9, 0]]]]]]]]) → y2
  11. If(IsInRegion[A, poly4], 1, If[IsInRegion[B, poly4], 2, If[IsInRegion[C, poly4], 3, If[IsInRegion[D, poly4], 4, If[IsInRegion[E, poly4], 5, If[IsInRegion[F, poly4], 6, If[IsInRegion[G, poly4], 7, If[IsInRegion[H, poly4], 8, If[IsInRegion[I, poly4], 9, 0]]]]]]]]) → x2
  12. If(IsInRegion[A, poly2], 1, If[IsInRegion[B, poly2], 2, If[IsInRegion[C, poly2], 3, If[IsInRegion[D, poly2], 4, If[IsInRegion[E, poly2], 5, If[IsInRegion[F, poly2], 6, If[IsInRegion[G, poly2], 7, If[IsInRegion[H, poly2], 8, If[IsInRegion[I, poly2], 9, 0]]]]]]]]) → y3
  13. If(IsInRegion[A, poly1], 1, If[IsInRegion[B, poly1], 2, If[IsInRegion[C, poly1], 3, If[IsInRegion[D, poly1], 4, If[IsInRegion[E, poly1], 5, If[IsInRegion[F, poly1], 6, If[IsInRegion[G, poly1], 7, If[IsInRegion[H, poly1], 8, If[IsInRegion[I, poly1], 9, 0]]]]]]]]) → x3
  14. Sequence(Point[{i + 0.1, 6}], i, -3, 5) → anchors
  15. Segment((1.1, -0.2), (1.1, 4)) → f
  16. Point({8, -2}) → fakeOrigin
  17. Sequence(Segment[fakeOrigin + ((gridSpacer * i), 0), fakeOrigin + ((gridSpacer * i), (10 * gridSpacer))], i, 1, 10) → verLines
  18. Sequence(Segment[fakeOrigin + (0, (gridSpacer * i)), fakeOrigin + ((gridSpacer * 10), (i * gridSpacer))], i, 1, 10) → horLines
  19. Vector(fakeOrigin, fakeOrigin + ((11 * gridSpacer), 0)) → xaxis
  20. Vector(fakeOrigin, fakeOrigin + (0, (11 * gridSpacer))) → yaxis
  21. Join({Sequence[(fakeOrigin * (1 - i / 300)) + ((x(point2anchor), y(fakeOrigin)) * i / 300), i, 0, 300], Sequence[((x(point2anchor), y(fakeOrigin)) * (1 - i / 300)) + (point2anchor * i / 300), i, 0, 300]}) → path2
  22. Element(path2, timer2) → mover2
  23. AreCollinear(point1anchor, point2anchor, point3anchor) → line
  24. Polygon((-0.3, -0.3), (2.5, -0.3), (2.5, 3.2), (-0.3, 3.2)) → region, h, i, j, k
  25. Join({Sequence[(fakeOrigin * (1 - i / 300)) + ((x(point3anchor), y(fakeOrigin)) * i / 300), i, 0, 300], Sequence[((x(point3anchor), y(fakeOrigin)) * (1 - i / 300)) + (point3anchor * i / 300), i, 0, 300]}) → path3
  26. Element(path3, timer3) → mover3
  27. Join({Sequence[(fakeOrigin * (1 - i / 300)) + ((x(point1anchor), y(fakeOrigin)) * i / 300), i, 0, 300], Sequence[((x(point1anchor), y(fakeOrigin)) * (1 - i / 300)) + (point1anchor * i / 300), i, 0, 300]}) → path1
  28. Element(path1, timer1) → mover1
  29. If(¬firstCheck, Line[mover1, mover2], Line[newMover1, newMover2]) → g
  30. Point({x(fakeOrigin) - gridSpacer, g(x(fakeOrigin) - gridSpacer)}) → leftBound
  31. Point({x(fakeOrigin) + (11 * gridSpacer), g(x(fakeOrigin) + (11 * gridSpacer))}) → rightBound
  32. If(¬firstCheck, Vector[mover1, leftBound], Vector[newMover1, leftBound]) → u
  33. If(¬firstCheck, Vector[mover1, rightBound], Vector[newMover1, rightBound]) → v
  34. If(¬firstCheck, timer3 ≟ Length[path3], checkedTimer ≟ 1) → ready

AI 绘图提示语参考

绘制一个坐标平面,包含水平和垂直的网格线以及坐标轴。在网格上放置三个可拖动的锚点,它们用于确定一条直线。从原点向每个锚点绘制路径,并显示沿路径移动的动点。根据三个锚点是否共线,显示一条直线或两条动点连线。在网格上放置九个标记点,用于检测它们所在的网格区域,并输出对应的行列编号。整个图形用于演示通过表格值绘制直线,并验证三点共线关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。