Chapter 8.3, Problem 42PPS

To determine

The coordinates of E.

Answer to Problem 42PPS

  $E=\left(-3-2\sqrt{3},-4\right)$

Explanation of Solution

Given:

  $30°-60°-90°$ triangle.

Calculation:

The graph of the points will be:

  $\overline{FG}$ is one of the long legs, therefore,

  $\begin{array}{l}FG=2-\left(-4\right)\\ FG=6\end{array}$

In $30°-60°-90°$ triangle,

  $\begin{array}{l}l=\sqrt{3}s\\ 6=\sqrt{3}s\\ s=\frac{6}{\sqrt{3}}\\ s=2\sqrt{3}\end{array}$

Point X is $2\sqrt{3}$ units away from F. Therefore, the coordinates of F will be:

  $E=\left(-3-2\sqrt{3},-4\right)$