# How do you find the distance between (6,2), (0,-6)?

Mar 8, 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:

$d = \sqrt{{\left(\textcolor{red}{0} - \textcolor{b l u e}{6}\right)}^{2} + {\left(\textcolor{red}{- 6} - \textcolor{b l u e}{2}\right)}^{2}}$

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

$d = \sqrt{36 + 64}$

$d = \sqrt{100} = 10$

The distance between the two points in $10$