Chapter 13.7, Problem 6PSA

To determine

To find:The coordinates of point C .

Answer to Problem 6PSA

The coordinate of point C is $\left(3,3\sqrt{3}\right)$

Explanation of Solution

Draw an equilateral triangle with each angle $60°$

In triangle ACD, the height of the equilateral triangle is calculated as,

  $\begin{array}{c}y=\sqrt{6^2-3^2}\\ =\sqrt{36-9}\\ =\sqrt{27}\\ =3\sqrt{3}\end{array}$

Therefore, the coordinate of point C is $\left(3,3\sqrt{3}\right)$