# What is the distance between (0,5) and (4,2)?

May 1, 2016

$5$

#### Explanation:

The distance $d$ between $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ is given by the distance formula:

$d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$

$= \sqrt{{\left(4 - 0\right)}^{2} + {\left(2 - 5\right)}^{2}}$

$= \sqrt{{4}^{2} + {\left(- 3\right)}^{2}}$

$= \sqrt{16 + 9}$

$= \sqrt{25}$

$= 5$