坐标变换下的直线方程探索

GeoGebra 命令及参数

1. TableText({{"0"}, {"\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ "}}, "hc") → Xt0
2. Corner(1) → corner1
3. Corner(3) → corner3
4. Corner(2) → corner2
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) - 10 / 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. Point(a) → A
15. Text("(x,y) = (" + (x(A)) + "," + (y(A)) + ") in black coordinate system") → text2
16. Text("(X,Y) = (" + (x(A) - x(O)) + "," + (y(A) - y(O)) + ") in blue coordinate system") → text1
17. Sequence(If[n ≟ 0, "", Text[TableText[{{"" + (n) + ""}, {"\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ "}}, "hc"], (n + x(O) - (Distance[Corner[Xt0, 1], Corner[Xt0, 2]] * 0.5) - 3 / unitX, y(O) - 2 / unitY), true, true]], n, (round((x(Corner[1]) - x(O)) / AxisStepX[]) * AxisStepX[]), x(Corner[2]) - x(O), AxisStepX[]) → XaxisNumbers
18. 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