[tex] \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}[/tex]
[tex] \bf -------------------------------\\\\
~~~~~~~~~~~~\textit{middle point of 2 points }
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(\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)
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\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) [/tex]