If P(2,4), Q(8,12), R(10,14) and S(x,y) are vertices of a parallelogram, then what is (x+y) equal to?

Explanation

The diagonals of a parallelogram bisect each other, meaning the midpoint of PR equals the midpoint of QS. Midpoint of PR is (\frac{2+10}{2}, \frac{4+14}{2}) = (6, 9). Midpoint of QS is (\frac{8+x}{2}, \frac{12+y}{2}). Equating them gives \frac{8+x}{2}=6 \implies x=4 and \frac{12+y}{2}=9 \implies y=6. Therefore, x+y = 4+6 = 10.

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