[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points}
\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ -2 &,& -3~)
% (c,d)
&&(~ 4 &,& 4~)
\end{array}
\\\\\\
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
d=\sqrt{[4-(-2)]^2+[4-(-3)]^2}\implies d=\sqrt{(4+2)^2+(4+3)^2}
\\\\\\
d=\sqrt{36+49}\implies \boxed{d=\sqrt{85}}\\\\
-------------------------------[/tex]
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points }
\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ -2 &,& -3~)
% (c,d)
&&(~ 4 &,& 4~)
\end{array}\qquad
% coordinates of midpoint
\left(\cfrac{ x_2 + x_1}{2}\quad ,\quad \cfrac{ y_2 + y_1}{2} \right)
\\\\\\
\left( \cfrac{4-2}{2}~~,~~\cfrac{4-3}{2} \right)\implies \left(\cfrac{2}{2}~~,~~\cfrac{1}{2} \right)\implies \boxed{\left(1~,~\frac{1}{2} \right)}[/tex]
