Question

What is the distance, d, between the points(2,7/2) and (5/3,1)?

Enter your answer in the box. Enter your answer in simplest radical form.

Answer 1

`~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{(7)/(2)})\qquad (\stackrel{x_2}{(5)/(3)}~,~\stackrel{y_2}{1})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ d=\sqrt{((5)/(3)-2)^2 + (1-(7)/(2))^2}\implies d=\sqrt{((-1)/(3))^2 + (-(5)/(2))^2} \\\\\\ d=\sqrt{\cfrac{1}{9}~~ + ~~\cfrac{25}{4}}\implies d=\sqrt{\cfrac{229}{36}}\implies d=\cfrac{√(229)}{√(36)}\implies d=\cfrac{√(229)}{6}`