# How do you find the distance between the points (3,7), (-2,-5)?

Jan 16, 2017

See the entire solution 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 two points in the problem and solving gives:

$d = \sqrt{{\left(\textcolor{red}{- 2} - \textcolor{b l u e}{3}\right)}^{2} + {\left(\textcolor{red}{- 5} - \textcolor{b l u e}{7}\right)}^{2}}$

$d = \sqrt{{\left(- 5\right)}^{2} + {\left(- 12\right)}^{2}}$

$d = \sqrt{25 + 144}$

$d = \sqrt{169}$

Or

$d = 13$