Question

What is the distance and midpoint of (-2,2)(2,-3)

Answer 1

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\(\stackrel{x_1}{-2}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}\\\\\\d=\sqrt{[2-(-2)]^2+[-3-2]^2}\implies d=\sqrt{(2+2)^2+(-3-2)^2}\\\\\\d=\sqrt{4^2+(-5)^2}\implies d=\sqrt{41}$

$\bf -------------------------------\\\\ ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-3})\qquad \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{2-2}{2}~~,~~\cfrac{-3+2}{2} \right)\implies \left( \cfrac{0}{2}~~,~~\cfrac{-1}{2} \right)\implies \left( 0~,~-\frac{1}{2} \right)$