# Math Help - Find a coordinate of a Paralellogram?

1. ## Find a coordinate of a Paralellogram?

2. Hello, rcfreak339!

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

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

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

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

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

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

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

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

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

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

The slopes are not negative reciprocals of each other.

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

Therefore, $ABCD$ 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...