Question

Points R(2,-1) and S(-5,3) are in the standard (x,y) coordinate plane. What is the length of RS in coordinate units?

Answer 1

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ R(\stackrel{x_1}{2}~,~\stackrel{y_1}{-1})\qquad S(\stackrel{x_2}{-5}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ RS=\sqrt{[-5-2]^2+[3-(-1)]^2}\implies RS=\sqrt{(-5-2)^2+(3+1)^2} \\\\\\ RS=\sqrt{49+16}\implies RS=\sqrt{65}$