If the vertices of a parallelogram $P Q R S$ taken in order are $P(3,4), Q(-2,3)$ and $R(-3,-2)$, th

Question

If the vertices of a parallelogram $P Q R S$ taken in order are $P(3,4), Q(-2,3)$ and $R(-3,-2)$, then the coordinates of its fourth vertex $S$ are\

Professor PC Thomas Classes · Answer

(c) : Let coordinates of $S$ is $(h, k)$. Diagonals of parallelogram bisects each other.\ $	herefore \quad\left(\frac{-3+3}{2}, \frac{-2+4}{2}ight) \equiv\left(\frac{h-2}{2}, \frac{k+3}{2}ight)$\ $\Rightarrow \quad(0,1) \equiv\left(\frac{h-2}{2}, \frac{k+3}{2}ight)$\ $	herefore h=2$ and $k=-1$\ So, the coordinates of $S$ is $(2,-1)$.