# What is the distance between (6,5) and (52,-12)?

May 22, 2018

See a 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:

$d = \sqrt{{\left(\textcolor{red}{52} - \textcolor{b l u e}{6}\right)}^{2} + {\left(\textcolor{red}{- 12} - \textcolor{b l u e}{5}\right)}^{2}}$

$d = \sqrt{{46}^{2} + {\left(- 17\right)}^{2}}$

$d = \sqrt{2116 + 289}$

$d = \sqrt{2405}$

$d = \sqrt{2405}$

Or

$d \cong 49.04$