Quadrilateral PQRS has vertices P(0,6), Q(-6,-2), R(2,-4), and S(4,2). Verify that the quadrilateral formed by joining the midpoints of the sides of PQRS is a parallelogram.

Answer 1

midpoints:

mPQ=A: (-3,2)
mQR=B: (-2,-3)
mRS=C: (3,-1)
mSP=D: (2,4)

check slopes:
AB: -5
BC: 2/5
CD: -5
DA: 2/5

parallel in pairs. OK.

Answer 2

Show tagt RSTU is a rectangle if the coordinates of tye vertices are respectively R(2,6) S(6,4) T(2,-4) and U(-2,-2)