1. ## parallelogram

Three vertices of a parallelogram are (1,1), (3,5), and (-1,4) . find all possible ordered pairs that could be the coordinates of the fourth vertex .

2. (-3,0), (5,2), (1,8)

3. 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 $\displaystyle \Delta ABC.$