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

Apr 15, 2018

$\implies d = 3 \sqrt{2}$

#### Explanation:

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

We are given:

$\implies \left({x}_{1} , {y}_{1}\right) = \left(2 , 5\right)$
$\implies \left({x}_{2} , {y}_{2}\right) = \left(5 , 2\right)$

Hence,

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

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

$\implies d = \sqrt{9 + 9}$

$\implies d = \sqrt{18}$

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

$\implies \textcolor{g r e e n}{d = 3 \sqrt{2}}$