Question

Determine the distance between the points (-2,3) and (5,- 3).

Answer 1

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[5-(-2)]^2+[-3-3]^2}\implies d=\sqrt{(5+2)^2+(-6)^2} \\\\\\ d=\sqrt{49+36}\implies d=\sqrt{85}\implies d \approx 9.22$