Chapter 16.1, Problem 2PS

To determine

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

Answer to Problem 2PS

The distance from the point to the graph of the given equation is $2\text{units}$ .

Explanation of Solution

Given information:

The given equation is,

  $3x+4y-10=0$

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

  $\begin{array}{c}d=\frac{\left|a{x}_1+b{y}_1+c\right|}{\sqrt{a^2+b^2}}\\ =\frac{\left|3\left(4\right)+\left(4\right)\left(2\right)+\left(-10\right)\right|}{\sqrt{{\left(3\right)}^2+{\left(4\right)}^2}}\\ =\frac{10}{5}\\ =2\text{units}\end{array}$

Thus, the distance from the point to the graph of the given equation is $2\text{units}$ .