# How do you use the distance formula to find the distance between (-10, 2) and (-4,-6)?

Feb 26, 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:

$d = \sqrt{{\left(\textcolor{red}{- 4} - \textcolor{b l u e}{- 10}\right)}^{2} + {\left(\textcolor{red}{- 6} - \textcolor{b l u e}{2}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{- 4} + \textcolor{b l u e}{10}\right)}^{2} + {\left(\textcolor{red}{- 6} - \textcolor{b l u e}{2}\right)}^{2}}$

$d = \sqrt{{6}^{2} + {\left(- 8\right)}^{2}}$

$d = \sqrt{36 + 64}$

$d = \sqrt{100} = 10$