# How do you find the distance between (7,5) and (-12,-1)?

Mar 22, 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:

$d = \sqrt{{\left(\textcolor{red}{- 12} - \textcolor{b l u e}{7}\right)}^{2} + {\left(\textcolor{red}{- 1} - \textcolor{b l u e}{5}\right)}^{2}}$

$d = \sqrt{{\left(- 19\right)}^{2} + {\left(- 6\right)}^{2}}$

$d = \sqrt{361 + 36}$

$d = \sqrt{397} = 19.925$ Rounded to the nearest hundredth.