# What is the distance between (2,5)  and (9,1)?

Dec 9, 2015

$\textcolor{w h i t e}{\times} \sqrt{65}$

#### Explanation:

Let distance be $d$. Then:

$\textcolor{w h i t e}{\times} {d}^{2} = {\left(\Delta x\right)}^{2} + {\left(\Delta y\right)}^{2} \textcolor{w h i t e}{\times \times \times \times \times x}$ (Pythagorous' Theorem)

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

$\implies d = \sqrt{{\left(\textcolor{red}{1} - \textcolor{red}{5}\right)}^{2} + {\left(\textcolor{red}{9} - \textcolor{red}{2}\right)}^{2}}$
$\textcolor{w h i t e}{\times x} = \sqrt{{\textcolor{red}{4}}^{2} + {\textcolor{red}{7}}^{2}}$
$\textcolor{w h i t e}{\times x} = \sqrt{\textcolor{red}{16} + \textcolor{red}{49}}$
$\textcolor{w h i t e}{\times x} = \sqrt{65}$