Chapter 16.1, Problem 6PS

To determine

To find: Thedistance from the point to the graph of the given equation.

Answer to Problem 6PS

The distance from the point to the graph of the given equation is $7.73\text{units}$ .

Explanation of Solution

Given information:

The given equation is,

  $x\cos 30°+y\sin 30°-8=0$

The distance from the point to the graph of the given equation is calculated as,

  $\begin{array}{c}d=\frac{\left|a{x}_1+b{y}_1+c\right|}{\sqrt{a^2+b^2}}\\ =\frac{\left|\cos 30°\left(-2\right)+\sin 30°\left(4\right)-8\right|}{\sqrt{{\left(\cos 30°\right)}^2+{\left(\sin 30°\right)}^2}}\\ =\frac{\left|-\sqrt{3}+2-8\right|}{1}\\ =7.73\text{units}\end{array}$

Thus, the distance from the point to the graph of the given equation is $7.73\text{units}$ .