[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points}
\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ 1 &,& 5~)
% (c,d)
&&(~ 3 &,& 9~)
\end{array}~~~
% distance value
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
d=\sqrt{(3-1)^2+(9-5)^2}\implies d=\sqrt{2^2+4^2}\implies d=\sqrt{20}
\\\\\\
d=\sqrt{4\cdot 5}\implies d=\sqrt{2^2\cdot 5}\implies d=2\sqrt{5}[/tex]
