# Thread: Find a coordinate of a Paralellogram?

1. ## Find a coordinate of a Paralellogram?

2. Hello, rcfreak339!

I don't suppose you made a sketch . . .

$\displaystyle ABCD$ is a parallelogram
with vertices: .$\displaystyle A(-2,1),\;B(2,-2),\;C(8,7),\;D(x,y)$

(a) Find the coordinates of point $\displaystyle D.$
Code:
              |   D
|   o
|   :
|   :           C
|   :           o (8,7)
|   :           :
(-2,1)   |   :           :
A o - - | - *           :9
- - - - - + - - - - - - - : - - -
|               :
|   B o - - - - *
|  (2,-2)  6
|

Since $\displaystyle ABCD$ lists the vertices in order,
. . the diagram shows the position of vertex $\displaystyle D.$

Going from $\displaystyle B$ to $\displaystyle C$, we move right 6, up 9.

Since $\displaystyle AD$ is parallel to $\displaystyle BC$, we must do the same from vertex $\displaystyle A.$

Moving "right 6, up 9" from $\displaystyle (-2,1)$ puts us at: .$\displaystyle D(4,10).$

(b) Determine if parallelogram $\displaystyle ABCD$ is a rectangle.
Compare the slopes of $\displaystyle AB$ and $\displaystyle BC.$

. . $\displaystyle m_{_{AB}} \:=\:\frac{-2 - 1}{2-(-2)} \:=\:-\frac{3}{4}$

. . $\displaystyle m_{_{BC}} \:=\:\frac{7-(-2)}{8-2} \:=\:\frac{9}{6} \:=\:\frac{3}{2}$

The slopes are not negative reciprocals of each other.

Hence, $\displaystyle AB$ is not perpendicular to $\displaystyle BC\!:\;\;\angle B \,\neq\,90^o$

Therefore, $\displaystyle ABCD$ is not a rectangle.

3. ^Thank you for the very informed and helpful post! I just am not very good at graphing and such, I can do Algebra any day but when t comes to Coordinates I am just not good...