Chapter 13.1, Problem 16PSB

To determine

To find: The fourth vertex if two sides are parallel to the x-axis.

Answer to Problem 16PSB

The possible points are $\left(-2,6\right)$ or $\left(16,6\right)$ .

Explanation of Solution

Given:

The vertex of the parallelogram are $\left(-5,-1\right)$ , $\left(4,-1\right)$ , and $\left(7,6\right)$ .

Calculation:

The y-coordinate of the fourth vertex must be 6 if two sides of the parallelogram are parallel to the x-axis. From the following diagram, the length of $\overline{\text{AB}}$ is $\overline{\text{AB}}=9$ (from distance formula).

  

Since opposite sides of parallelograms are $\cong$ , then the x-coordinate of the last vertex must be $7\pm 9$ , or $-2$ or $16$ .

Therefore, the possible points are $\left(-2,6\right)$ or $\left(16,6\right)$ .