Hello, Zharif93!
Did you make a sketch?
The answer jumps out at you!
$\displaystyle P(\text{-}3,2),\;Q(2,\text{-}2),\;R(3,1),\; S(x,y)$ are the vertices of a parallelogram.
Find the values of $\displaystyle x$ and $\displaystyle y$ Code:
S |
(x,y)o |
/↑ * |
/ ↑ *
/ ↑ | *
/ ↑ | *
P / ↑ | * R
(-3,2)o → → + | o (3,1)
* | *↑
- - - - - - * - - + - - - - * ↑ - - - -
* | * ↑ 3
* * ↑
| * * 1 ↑
| o → → +
| (2,-2)
| Q
Assuming that parallelgram $\displaystyle PQRS$ has its vertices in order,
. . we see that vertex $\displaystyle S$ is in the upper-left.
Going from Q to R, we move 1 unit right, 3 units up.
Since $\displaystyle PS \parallel QR$, going from $\displaystyle P$ to $\displaystyle S$,
. . we also move 1 unit right, 3 units up.
Therefore, vertex $\displaystyle S$ is at $\displaystyle (-2,5).$