Chapter 16.2, Problem 5PS

To determine

To find: Thepossible values of $x$ .

Answer to Problem 5PS

The possible values of $x$ are $-\frac{76}{11}\text{or }\frac{92}{11}$ .

Explanation of Solution

Given information:

The coordinates of the vertices of the triangle are $\left(-2,6\right),\left(4,17\right),\text{and}\left(x,11\right)$ . The area of the triangle is $42$ .

The area of $\Delta TRY$ is calculated as,

  $\begin{array}{l}A=\frac{1}{2}\left|\left(-2\right)\left(17\right)+4\left(11\right)+6x-\left(-2\right)\left(11\right)-4\left(6\right)-17x\right|\\ 42=\frac{1}{2}\left|\left(-2\right)\left(17\right)+4\left(11\right)+6x-\left(-2\right)\left(11\right)-4\left(6\right)-17x\right|\\ 84=\left|8-11x\right|\\ x=-\frac{76}{11}\text{or }\frac{92}{11}\end{array}$

Thus, the possible values of $x$ are $-\frac{76}{11}\text{or }\frac{92}{11}$ .