# How do you find the distance between (0, -4) and (4,4)?

Jun 21, 2017

$4 \sqrt{5}$

#### Explanation:

Use the distance formula:

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

Plug your points into the formula.

You can make either coordinate set #1. Let's use (0, -4) as our first.

$\left(0 , - 4\right)$
${x}_{1} = 0 , {y}_{1} = - 4$

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

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

$= \sqrt{{4}^{2} + {8}^{2}}$
$= \sqrt{16 + 64}$
$= \sqrt{80}$
$= \sqrt{5} \cdot \sqrt{16}$
$= \sqrt{5} \cdot 4$
$= 4 \sqrt{5}$

The distance between the two points is $4 \sqrt{5}$.