# What is the distance between (8, 2)  and  (–5, 13) ?

Dec 21, 2015

$\sqrt{290}$ units

#### Explanation:

The distance between two points can be calculated with the formula:

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

where:
$d =$distance
$\left({x}_{1} , {y}_{1}\right) = \left(8 , 2\right)$
$\left({x}_{2} , {y}_{2}\right) = \left(- 5 , 13\right)$

Substitute your known values into the distance formula to find the distance between the two points:

$d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$
$d = \sqrt{{\left(\left(- 5\right) - \left(8\right)\right)}^{2} + {\left(\left(13\right) - \left(2\right)\right)}^{2}}$
$d = \sqrt{{\left(- 13\right)}^{2} + {\left(11\right)}^{2}}$
$d = \sqrt{169 + 121}$
$d = \sqrt{290}$

$\therefore$, the distance between the two points is $\sqrt{290}$ units.