# What is the distance between (2,-4) and (-1,-1)?

Apr 16, 2018

The distance is $3 \sqrt{2}$.

#### Explanation:

The distance formula is:
$d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$

Since we have the value of two points, we can plug them into the distance formula:

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

And now simplify:
$d = \sqrt{{\left(- 3\right)}^{2} + {\left(- 1 + 4\right)}^{2}}$

$d = \sqrt{9 + {\left(3\right)}^{2}}$

$d = \sqrt{9 + 9}$

$d = \sqrt{18}$

$d = \sqrt{9 \cdot 2}$

$d = \sqrt{9} \cdot \sqrt{2}$

$d = 3 \sqrt{2}$

The distance is $3 \sqrt{2}$.

Hope this helps!