# What is the distance between (3, 5) and  (–5, 13) ?

Dec 11, 2015

Apply the distance formula to find that the distance is $8 \sqrt{2}$

#### Explanation:

Applying the Distance Formula with $\left({x}_{1} , {y}_{1}\right) = \left(3 , 5\right)$ and $\left({x}_{2} , {y}_{2}\right) = \left(- 5 , 13\right)$ gives us

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

$= \sqrt{{\left(- 5 - 3\right)}^{2} + {\left(13 - 5\right)}^{2}}$

$= \sqrt{64 + 64}$

$= \sqrt{128} = 8 \sqrt{2}$