Question

Given square TECH with T(-1,3) and E(-2,-3), find the perimeter of the square in the simplest radical form.

Answer 1

Check the picture below, so the square looks more or less like so, since it has all equal sides, then we can simply get the distance of TE and multiply it times 4 and that's the perimeter.

$~~~~~~~~~~~~\textit{distance between 2 points} \\\\ T(\stackrel{x_1}{-1}~,~\stackrel{y_1}{3})\qquad E(\stackrel{x_2}{-2}~,~\stackrel{y_2}{-3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ TE=\sqrt{[-2 - (-1)]^2 + [-3 - 3]^2}\implies TE=\sqrt{(-2+1)^2+(-6)^2} \\\\\\ TE=\sqrt{(-1)^2+(-6)^2}\implies TE=\sqrt{37}~\hfill \stackrel{\textit{4 times that much}}{4\sqrt{37}}$