# What is the distance between the points (6,8) and (3,4)?

Feb 12, 2017

The distance between the points is $\sqrt{29}$ or $5.385$ 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:

$d = \sqrt{{\left(\textcolor{red}{4} - \textcolor{b l u e}{6}\right)}^{2} + {\left(\textcolor{red}{3} - \textcolor{b l u e}{8}\right)}^{2}}$

$d = \sqrt{{\left(- 2\right)}^{2} + {\left(- 5\right)}^{2}}$

$d = \sqrt{4 + 25}$

$d = \sqrt{29} = 5.385$ rounded to the nearest thousandth.