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. (1 point) P(); R()

Answer 1

To find the coordinates of vertices P and R, we need to determine the points that are diagonally opposite from points Q and S.

Let's calculate the midpoint of line segment QS:
Midpoint: ((x1+x2)/2, (y1+y2)/2)
Midpoint: ((4+(-1))/2, (-2+3)/2)
Midpoint: (3/2, 1/2)

Now, we can use the midpoint and the given points Q and S to find points P and R:

Point P:
Since the midpoint is at (3/2, 1/2) and Q is at (4, -2), we can calculate P as follows:
P: (2(3/2) - 4, 2(1/2) - (-2))
P: (3-4, 1+2)
P: (-1, 3)

Point R:
Since the midpoint is at (3/2, 1/2) and S is at (-1, 3), we can calculate R as follows:
R: (2(3/2) - (-1), 2(1/2) - 3)
R: (3 + 1, 1 - 3)
R: (4, -2)

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