Question

Find the distance between the two points in simplest radical form.
(-5, -4) and (3, – 7)

Answer 1

$~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[3 - (-5)]^2 + [-7 - (-4)]^2}\implies d=\sqrt{(3+5)^2 + (-7+4)^2} \\\\\\ d=\sqrt{8^2 + (-3)^2}\implies d=\sqrt{64+9}\implies d=\sqrt{73}$