9514 1404 393
Explanation:
The quadrilateral is a parallelogram if the midpoints of its diagonals are the same point. That is, if ...
(N +Q)/2 = (P +R)/2
Multiplying by 2, we can simplify the test to ...
N +Q = P +R
(5, 1) +(6, 9) = (2, 7) +(9, 3)
(5+6, 1+9) = (2+9, 7+3)
(11, 10) = (11, 10) . . . . . . . true ∴ NPQR is a parallelogram
