# What is the distance between (5, 12) and (10, 2) ?

Dec 14, 2015

$\textcolor{w h i t e}{\times} 5 \sqrt{5}$

#### 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)

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

$\implies d = \sqrt{{\left(\textcolor{red}{10} - \textcolor{red}{5}\right)}^{2} + {\left(\textcolor{red}{2} - \textcolor{red}{12}\right)}^{2}}$
$\textcolor{w h i t e}{\times x} = \sqrt{{\textcolor{red}{5}}^{2} + {\textcolor{red}{10}}^{2}}$
$\textcolor{w h i t e}{\times x} = \sqrt{\textcolor{red}{25} + \textcolor{red}{100}}$
$\textcolor{w h i t e}{\times x} = 5 \sqrt{5}$