# What is the distance between (5, –1) and  (-4, 6) ?

Jun 6, 2018

$d = \sqrt{130}$

#### Explanation:

Distance:

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

We have:

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

and

$\left({x}_{2} , {y}_{2}\right) = \left(- 4 , 6\right)$

This gives us a distance of

$d = \sqrt{{\left(6 - \left(- 1\right)\right)}^{2} + {\left(- 4 - 5\right)}^{2}}$

$d = \sqrt{{\left(7\right)}^{2} + {\left(- 9\right)}^{2}}$

$d = \sqrt{49 + 81}$

$d = \sqrt{130}$