Check the picture below.
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{2})\qquad B(\stackrel{x_2}{1}~,~\stackrel{y_2}{4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{[1-(-4)]^2+[4-2]^2}\implies AB=\sqrt{(1+4)^2+(4-2)^2} \\\\\\ AB=\sqrt{5^2+2^2}\implies AB=\sqrt{25+4}\implies \boxed{AB=\sqrt{29}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ B(\stackrel{x_2}{1}~,~\stackrel{y_2}{4})\qquad C(\stackrel{x_2}{2}~,~\stackrel{y_2}{-1})~\hfill BC=\sqrt{(2-1)^2+(-1-4)^2} \\\\\\ BC=\sqrt{1^2+(-5)^2}\implies BC=\sqrt{1+25}\implies \boxed{BC=\sqrt{26}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \sqrt{29}~~\ne~~\sqrt{26}~\hfill[/tex]
