# How do you find the distance between (-7,5) and (1,-1)?

May 13, 2017

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:

$d = \sqrt{{\left(\textcolor{red}{1} - \textcolor{b l u e}{- 7}\right)}^{2} + {\left(\textcolor{red}{- 1} - \textcolor{b l u e}{5}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{1} + \textcolor{b l u e}{7}\right)}^{2} + {\left(\textcolor{red}{- 1} - \textcolor{b l u e}{5}\right)}^{2}}$

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

$d = \sqrt{64 + 36}$

$d = \sqrt{100}$

$d = 10$