# What is the distance between (15,-4) and (12,14)?

Mar 3, 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:

$d = \sqrt{{\left(\textcolor{red}{12} - \textcolor{b l u e}{15}\right)}^{2} + {\left(\textcolor{red}{14} - \textcolor{b l u e}{- 4}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{12} - \textcolor{b l u e}{15}\right)}^{2} + {\left(\textcolor{red}{14} + \textcolor{b l u e}{4}\right)}^{2}}$

$d = \sqrt{{\left(- 3\right)}^{2} + {18}^{2}}$

d = sqrt((9 + 324)

$d = \sqrt{333}$

$d = \sqrt{9 \times 37}$

$d = \sqrt{9} \sqrt{37}$

$d = 3 \sqrt{37}$