Chapter 16.1, Problem 3PS

To determine

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

Answer to Problem 3PS

The distance from the point to the graph of the given equation is $2.24\text{units}$ .

Explanation of Solution

Given information:

The given equation is,

  $7x-24y+2=0$

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

  $\begin{array}{c}d=\frac{\left|a{x}_1+b{y}_1+c\right|}{\sqrt{a^2+b^2}}\\ =\frac{\left|7\left(2\right)+\left(-24\right)\left(3\right)+\left(2\right)\right|}{\sqrt{{\left(7\right)}^2+{\left(-24\right)}^2}}\\ =\frac{56}{25}\\ =2.24\text{units}\end{array}$

Thus, the distance from the point to the graph of the given equation is $2.24\text{units}$ .