# How do you find the distance between points (-3,5), (5,-3)?

Jan 28, 2017

Use the formula for distance, see 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 given in the problem produces:

$d = \sqrt{{\left(\textcolor{red}{5} - \textcolor{b l u e}{- 3}\right)}^{2} + {\left(\textcolor{red}{- 3} - \textcolor{b l u e}{5}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{5} + \textcolor{b l u e}{3}\right)}^{2} + {\left(\textcolor{red}{- 3} - \textcolor{b l u e}{5}\right)}^{2}}$

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

$d = \sqrt{64 + 64}$

$d = \sqrt{128} = 11.314$ rounded to the nearest thousandth.