[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ -5 &,& 1~)
% (c,d)
&&(~ -2 &,& 3~)
\end{array}~~
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
d=\sqrt{[-2-(-5)]^2+[3-1]^2}\implies d=\sqrt{(-2+5)^2+(3-1)^2}
\\\\\\
d=\sqrt{3^2+2^2}\implies d=\sqrt{13}[/tex]
