# How do you find the distance between points (5,1), (0,4)?

Jan 16, 2017

See entire process below:

#### 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 points from the problem gives:

$d = \sqrt{{\left(\textcolor{red}{0} - \textcolor{b l u e}{5}\right)}^{2} + {\left(\textcolor{red}{4} - \textcolor{b l u e}{1}\right)}^{2}}$

$d = \sqrt{{\left(- 5\right)}^{2} + {\left(3\right)}^{2}}$

$d = \sqrt{25 + 9}$

$d = \sqrt{34}$

Or

$d = 5.83$ rounded to the nearest hundredth.