Question

Rectangle PQRS has vertices Q(4,−2) and S(−1,3). What are the coordinates of vertices P and R? Note, the vertex labels are located counterclockwise on the graph.

Answer 1

To find the coordinates of vertices P and R, we need to determine the opposite points of the rectangle.

Given:
Q(4, -2) and S(-1, 3)

To find P:
Let's consider the x-coordinate of Q and the y-coordinate of S to determine the x-coordinate of P. This means that the x-coordinate of P will be the same as Q's: x = 4.
Similarly, the y-coordinate of P will be the same as S's: y = 3.

Therefore, the coordinates of vertex P are (4, 3).

To find R:
Let's consider the y-coordinate of Q and the x-coordinate of S to determine the y-coordinate of R. This means that the y-coordinate of R will be the same as Q's: y = -2.
Similarly, the x-coordinate of R will be the same as S's: x = -1.

Therefore, the coordinates of vertex R are (-1, -2).

Therefore, the coordinates of vertices P and R are P(4, 3) and R(-1, -2), respectively.