Rationale
The point (-1,1) lies in the shaded region of the xy-plane above.
This point, when plotted on a Cartesian plane, falls within the given shaded region. The x-coordinate and y-coordinate of this point correspond respectively to -1 and 1, placing it within the boundaries of the shaded area.
A) (-1,1)
This is the correct answer. The coordinates (-1,1) fall within the shaded region of the xy-plane when plotted accordingly. The x-coordinate is -1 and the y-coordinate is 1, both of which place the point inside the shaded region.
B) (0,1)
The coordinates (0,1) do not fall within the shaded region. The x-coordinate is 0 and the y-coordinate is 1, which lie outside of the boundaries of the shaded area.
C) (1,2)
The coordinates (1,2) do not fall within the shaded region. The x-coordinate is 1 and the y-coordinate is 2, which also lie outside of the boundaries of the shaded area.
D) (2,-1)
The coordinates (2,-1) do not fall within the shaded region. The x-coordinate is 2 and the y-coordinate is -1, which place the point outside of the boundaries of the shaded area.
Conclusion
In the context of the xy-plane, a point is defined by its x (horizontal) and y (vertical) coordinates. The point (-1,1) is the only one among the provided options that falls within the boundaries of the shaded region when plotted on the plane. All the other points, namely (0,1), (1,2), and (2,-1) are located outside the shaded area. Therefore, the point (-1,1) is the correct answer.