Hello, sri340!
Three vertices of a parallelogram are: A(1,1), B(3,5), and C(1,4).
Find all possible ordered pairs that could be the coordinates of the fourth vertex . This can be solved without any fancy formulas . . . Code:
 B
 (3,5)
 o
 * * *
C * * *
o  * *
(1,4)*  * *
*  * o D
* * *
 * * *
 o
 (1,1)
 A
     +             

Suppose vertex $\displaystyle D$ is to the right, as shown in the diagram.
Going from $\displaystyle C$ to $\displaystyle B$, we move: right 4, up 1.
Since $\displaystyle AD \parallel CB$, going from $\displaystyle A$ to $\displaystyle D$, we make the same moves.
Therefore: .$\displaystyle A(1,1) + (\text{right 4, up 1}) \;=\;D(5,2)$
There are two more possible locations for vertex $\displaystyle D$:
. . left and above $\displaystyle \Delta ABC$, and left and below $\displaystyle \Delta ABC.$