Question

Lyle is camping at a campground. Lyle's cabin is represented by the point (-27,23). The dining hall is located 21 meters east and 20 meters south of Lyle's cabin and is represented by the point (-6,3).
The shortest distance from Lyle's cabin to the dining hall is_____meters.

Answer 1

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \stackrel{\textit{Lyle's cabin}}{(\stackrel{x_1}{-27}~,~\stackrel{y_1}{23})}\qquad \stackrel{\textit{dining hall}}{(\stackrel{x_2}{-6}~,~\stackrel{y_2}{3})}\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-6-(-27)]^2+[3-23]^2}\implies d=\sqrt{(-6+27)^2+(3-23)^2} \\\\\\ d=\sqrt{21^2+(-20)^2}\implies d=\sqrt{841}\implies d=29$