# How do you find the distance between (16,-6), (1,2)?

Jan 26, 2017

See the 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 value from the points in the problem gives:

$d = \sqrt{{\left(\textcolor{red}{1} - \textcolor{b l u e}{16}\right)}^{2} + {\left(\textcolor{red}{2} - \textcolor{b l u e}{- 6}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{1} - \textcolor{b l u e}{16}\right)}^{2} + {\left(\textcolor{red}{2} + \textcolor{b l u e}{6}\right)}^{2}}$

$d = \sqrt{- {15}^{2} + {8}^{2}}$

$d = \sqrt{225 + 64}$

$d = \sqrt{289} = 17$