[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-5-1]^2+[2-(-6)]^2}\implies d=\sqrt{(-5-1)^2+(2+6)^2} \\\\\\ d=\sqrt{(-6)^2+8^2}\implies d=\sqrt{36+64}\implies d=\sqrt{100}\implies d=10 \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{9})\qquad B(\stackrel{x_2}{-1}~,~\stackrel{y_2}{6})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{[-1-(-3)]^2+[6-9]^2}\implies AB=\sqrt{(-1+3)^2+(6-9)^2} \\\\\\ AB=\sqrt{2^2+(-3)^2}\implies AB=\sqrt{13}\implies AB\approx 3.6[/tex]
