[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points}
\\\\
A(\stackrel{x_1}{4}~,~\stackrel{y_1}{5})\qquad
B(\stackrel{x_2}{1}~,~\stackrel{y_2}{2})\qquad \qquad
% distance value
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
AB=\sqrt{(1-4)^2+(2-5)^2}\implies AB=\sqrt{(-3)^2+(-3)^2}
\\\\\\
AB=\sqrt{9+9}\implies \boxed{AB=\sqrt{18}}\implies AB=\sqrt{2(9)}
\\\\\\
AB=\sqrt{2(3^2)}\implies \implies AB=3\sqrt{2}[/tex]
