Question

Three points P(-2,1), Q(-6,4), and R(4,3) are three vertices of a parallelogram PQRS. Use your knowledge on the magnitude of vectors to find a possible coordinate for S.

Answer 1

PQ = Q-P = -4i+3j
QR = R-Q = 10i-j
so, since
|PS| = |QR| and PS||QR,
S-P = 10i-j
S = P+R-Q = (-2,1)+(10,-1) = (8,0)
another arrangement gives S = (0,6)

Answer 2

oh thank you! but what would be the other arrangement that would give (0,6), i think that's the one they're looking for

Answer 3

If you order the vertices PRQS you get (0,6)
Plot the points to see this.