Problem: Three vertices of parallelogram PQRS are P(−3,−2),Q(1,−5),R(9,1) with P and R diagonally opposite. The sum of the coordinates of vertex S is:
Answer Choices:
A. 13
B. 12
C. 11
D. 10
E. 9
Solution:
The sum of the x-coordinates of P and R equals the sum of the x-coordinates of Q and S, and, similarly, for the y-coordinates. ∴x+1=6,x=5 and y−5=−1,y=4∴x+y=9
or
Let Sx be the x-coordinate of S and Sy, the y-coordinate of S, and, similarly, for P,Q, and R. Then, by congruent triangles. Qx−Rx=Px−Sx,1−9=−3−Sx,Sx=5. Similarly Sy=4. ∴Sx+Sy=9.