[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ 1 &,& 3~)
% (c,d)
&&(~ -3 &,& -1~)
\end{array}~~~
% distance value
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
d=\sqrt{(-3-1)^2+(-1-3)^2}\implies d=\sqrt{(-4)^2+(-4)^2}
\\\\\\
d=\sqrt{32}\implies d=\sqrt{16\cdot 2}\implies d=\sqrt{4^2\cdot 2}\implies d=4\sqrt{2}[/tex]
