Question 16

The point (-1,1) lies in the shaded region of the xy-plane above.

The point (-1,1) is located in the shaded region of the xy-plane as it meets the criteria established by the boundaries of that region.

A) (-1,1)

This point is in the shaded region as it satisfies the conditions set by the inequalities defining that area. Specifically, the coordinates (-1,1) indicate that x is negative and y is positive, which aligns with the shading in the diagram.

B) (0,1)

While this point has a positive y-coordinate, it lies on the y-axis where x equals zero. Depending on the specific boundaries of the shaded region, this point may not fall within the shaded area, making it incorrect.

C) (1,2)

This point is located in the first quadrant, where both x and y are positive. However, it may not satisfy the necessary conditions of the shaded region above, thus it is not a correct choice.

D) (2,-1)

The coordinates of this point indicate that x is positive and y is negative, placing it in the fourth quadrant. Since the shaded region is defined differently, this point cannot be part of that area.

Conclusion

The point (-1,1) is definitively the correct answer as it is the only option that meets the criteria for lying within the shaded region. All other options fail to satisfy the conditions set by the boundaries of the shaded area, either falling outside or on the axes where the shading does not apply.