Final answer:
In order for quadrilateral PQRS to be a parallelogram, the opposite sides must be parallel. The slopes of the sides must be equal. Without the given coordinates or additional information, it is not possible to determine the values of a and b. Therefore, the correct answer is D. not enough information.
Step-by-step explanation:
In order for quadrilateral PQRS to be a parallelogram, the opposite sides must be parallel.
This means that Segment PQ is parallel to Segment RS and Segment PS is parallel to Segment QR.
Therefore, the slope of Segment PQ must be equal to the slope of Segment RS, and the slope of Segment PS must be equal to the slope of Segment QR.
Slope is represented by the formula m = (y2 - y1) / (x2 - x1).
Therefore, in order for PQRS to be a parallelogram, the values of a and b must make the slopes of the sides equal.
Without the given coordinates or additional information, it is not possible to determine the values of a and b.
Therefore, the correct answer is D. not enough information.