# How do you find the distance when given two coordinate points?

Nov 6, 2014

Distance Formula

The distance $D$ between two points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ can be found by

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

Example

Find the distance between the points $\left(1 , - 2\right)$ and $\left(5 , 1\right)$.

Let $\left({x}_{1} , {y}_{1}\right) = \left(1 , - 2\right)$ and $\left({x}_{2} , {y}_{2}\right) = \left(5 , 1\right)$.

By Distance Formula above,

$D = \sqrt{{\left(5 - 1\right)}^{2} + {\left[1 - \left(- 2\right)\right]}^{2}} = \sqrt{16 + 9} = \sqrt{25} = 5$

I hope that this was helpful.