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坐标系变换对点坐标的影响

坐标系变换对点坐标的影响
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2014-02-23 20:52
解析几何变换几何作图
①本范例演示了改变坐标系原点对单个点坐标的影响；②涉及的核心数学概念为坐标系的变换、点的坐标表示；③作图要点：使用了TableText, Corner, Distance, Text, Line, Sequence等GeoGebra命令和对象；④适合高中数学学生探索坐标系变换的几何意义。

GeoGebra 命令及参数

  1. TableText({{"0"}, {"\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ "}}, "hc") → Xt0
  2. Corner(1) → corner1
  3. Corner(2) → corner2
  4. Corner(3) → corner3
  5. Corner(4) → corner4
  6. Corner(5) → screenDim
  7. Distance(corner1, corner2) → distX
  8. Distance(corner1, corner4) → distY
  9. Text("$(x_1,y_1)=(" + (x(O)) + "," + (y(O)) + ")$", (x(O), y(O) - 12 / unitY), true, true) → text3
  10. Line(O, xAxis) → XaxisLine
  11. Sequence(Segment[(n + x(O), y(O)), (n + x(O), y(O) - 2 / unitY)], n, (round((x(Corner[1]) - x(O)) / AxisStepX[]) * AxisStepX[]), x(Corner[2]) - x(O), AxisStepX[]) → XaxisTicks
  12. Line(O, yAxis) → YaxisLine
  13. Sequence(Segment[(x(O), y(O) + n), (x(O) - 2 / unitX, y(O) + n)], n, (round((y(Corner[1]) - y(O)) / AxisStepY[]) * AxisStepY[]), y(Corner[4]) - y(O), AxisStepY[]) → YaxisTicks
  14. Text("(x,y) = (" + (x(A)) + "," + (y(A)) + ") in black coordinate system") → text2
  15. Text("(X,Y) = (" + (x(A) - x(O)) + "," + (y(A) - y(O)) + ") in blue coordinate system") → text1
  16. Sequence(If[n ≟ 0, "", Text[TableText[{{"" + (n) + ""}, {"\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ "}}, "hc"], (n + x(O) - (Distance[Corner[Xt0, 1], Corner[Xt0, 2]] * 0.5) - 4 / unitX, y(O) - 2 / unitY), true, true]], n, (round((x(Corner[1]) - x(O)) / AxisStepX[]) * AxisStepX[]), x(Corner[2]) - x(O), AxisStepX[]) → XaxisNumbers
  17. Sequence(If[n ≟ 0, "", Text[TableText[{{"\phantom{(}" + (n) + ""}, {"\phantom{(} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ "}}, "hr"], (x(O) - Distance[Corner[Xt0, 1], Corner[Xt0, 2]] - 4 / unitX, n + y(O) + (Distance[Corner[Xt0, 1], Corner[Xt0, 4]] * 0.25) + 1 / unitY), true, true]], n, (round((y(Corner[1]) - y(O)) / AxisStepY[]) * AxisStepY[]), y(Corner[4]) - y(O), AxisStepY[]) → YaxisNumbers