Chapter 5.7, Problem 24PSB

To determine

Tocalculate: the value of $x$ .

Answer to Problem 24PSB

  $x=-3$

Explanation of Solution

Given information:

  $D$ is the reflection of $E\left(x,14\right)$ across the $y-axis$ and $\overleftrightarrow{CD}\parallel \overleftrightarrow{AB}$

Formula used:

The slope the line joining $\left(x_1,y_1\right)\text{ and }\left(x_2,y_2\right)$ is $\frac{y_2-y_1}{x_2-x_1}$ .

Calculation:

Given that $D$ is the reflection of $E\left(x,14\right)$ across the $y-axis$ implies $D=\left(-x,14\right)$

The slope of $\overleftrightarrow{AB}$ with $A\left(0,-4\right)\text{ and }B\left(3,0\right)$ is $\frac{0-\left(-4\right)}{3-0}=\frac{4}{3}$

Given that $\overleftrightarrow{CD}$ is parallel to $\overleftrightarrow{AB}$ .

  $\begin{array}{l}\Rightarrow \text{The slope of }\overleftrightarrow{CD}\text{ =The slope of }\overleftrightarrow{AB}\\ \Rightarrow \text{The slope of }\overleftrightarrow{CD}\text{ =}\frac{4}{3}\\ \Rightarrow \frac{14-10}{-x-0}=\frac{4}{3}\\ \Rightarrow \frac{4}{-x}=\frac{4}{3}\\ \Rightarrow x=-3\end{array}$