# How do you find the distance between the points (-3,8), (5,4)?

Feb 19, 2017

The distance between the points is $\sqrt{65}$ or $8.062$ rounded to the nearest thousandth.

#### Explanation:

The formula for calculating the distance between two points is:

$d = \sqrt{{\left(\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}\right)}^{2} + {\left(\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}\right)}^{2}}$

Substituting the values from the points in the problem gives:

$d = \sqrt{{\left(\textcolor{red}{4} - \textcolor{b l u e}{- 3}\right)}^{2} + {\left(\textcolor{red}{4} - \textcolor{b l u e}{8}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{4} + \textcolor{b l u e}{3}\right)}^{2} + {\left(\textcolor{red}{4} - \textcolor{b l u e}{8}\right)}^{2}}$

$d = \sqrt{{7}^{2} + {\left(- 4\right)}^{2}}$

$d = \sqrt{49 + 16}$

$d = \sqrt{65} = 8.062$ rounded to the nearest thousandth.