# What is the distance of the A(-2,1) and B(5,3)?

Mar 7, 2017

See the entire solution 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 values from the points in the problem gives:

$d = \sqrt{{\left(\textcolor{red}{5} - \textcolor{b l u e}{- 2}\right)}^{2} + {\left(\textcolor{red}{3} - \textcolor{b l u e}{1}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{5} + \textcolor{b l u e}{2}\right)}^{2} + {\left(\textcolor{red}{3} - \textcolor{b l u e}{1}\right)}^{2}}$

$d = \sqrt{{7}^{2} + {2}^{2}}$

$d = \sqrt{49 + 4}$

$d = \sqrt{53} = 7.280$

The distance is $\sqrt{53}$ or $7.280$ rounded to the nearest thousandth