1. ## [SOLVED]parallelogram

P(-3,2) Q(2,-2) R(3,1) S(x,y) are the vertices of a parallelogram .Find
the values of x and y

2. Hello Zharif,
This is an oft repeated problem so you could scan thru current and past answers. For immediate help try this.

Plot the three points.Connect PR ang RQ. Note that two parallelograms can be constructed where x,y are in different quadrants.Draw a line thru P approx parallel to RQ. What is the slope of this line .x,y must lie on it. Proceed and report.

bjh

3. Hello, Zharif93!

Did you make a sketch?
The answer jumps out at you!

$P(\text{-}3,2),\;Q(2,\text{-}2),\;R(3,1),\; S(x,y)$ are the vertices of a parallelogram.
Find the values of $x$ and $y$
Code:
           S        |
(x,y)o     |
/↑  *  |
/ ↑     *
/  ↑     |  *
/   ↑     |     *
P   /    ↑     |        *      R
(-3,2)o → → +     |           o (3,1)
*        |          *↑
- - - - - - * - - + - - - - * ↑ - - - -
*  |        *  ↑ 3
*       *   ↑
|  *   * 1  ↑
|     o → → +
|  (2,-2)
|     Q

Assuming that parallelgram $PQRS$ has its vertices in order,
. . we see that vertex $S$ is in the upper-left.

Going from Q to R, we move 1 unit right, 3 units up.

Since $PS \parallel QR$, going from $P$ to $S$,
. . we also move 1 unit right, 3 units up.

Therefore, vertex $S$ is at $(-2,5).$