# What is the distance between (-3,2) and (2,-2)?

Dec 21, 2015

$\sqrt{41}$

#### Explanation:

Based on the Pythagorean Theorem the distance between two points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ is given by the formula:
$\textcolor{w h i t e}{\text{XXX}} d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$

For the given example:
$\textcolor{w h i t e}{\text{XXX}} d = \sqrt{{\left(2 - \left(- 3\right)\right)}^{2} + {\left(\left(- 2\right) - 2\right)}^{2}}$

$\textcolor{w h i t e}{\text{XXX}} = \sqrt{{5}^{2} + {\left(- 4\right)}^{2}}$

$\textcolor{w h i t e}{\text{XXX}} = \sqrt{25 + 16}$

$\textcolor{w h i t e}{\text{XXX}} = \sqrt{41}$