Chapter 13.7, Problem 19PSB

To determine

To find: The length of the altitude from D to line EF.

Answer to Problem 19PSB

The length of the altitude is $\frac{24}{5}$ .

Explanation of Solution

Given:

The vertices of the triangle DEF are $D=\left(1,2\right)$ , $E=\left(7,2\right)$ and $F\left(1,10\right)$ >

Calculation:

Consider the area of the triangle $DEF$ is,

  $\begin{array}{c}A=\frac{6\left(8\right)}{2}\\ =24\end{array}$

Consider the distance between the points E to F is,

  $\begin{array}{c}EF=\sqrt{{\left(1-7\right)}^2+{\left(10-2\right)}^2}\\ =\sqrt{36+64}\\ =10\end{array}$

Then, the formula for the area is,

  $\begin{array}{l}\frac{1}{2}EF\left(\text{alt}\text{to}EF\right)=24\\ \left(\text{alt}\text{to}EF\right)=\frac{24\left(2\right)}{10}\\ \left(\text{alt}\text{to}EF\right)=\frac{24}{5}\end{array}$