[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&C&(~ -3 &,& 1~)
% (c,d)
&D&(~ 5 &,& 6~)
\end{array}~
% distance value
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
CD=\sqrt{[5-(-3)]^2+[6-1]^2}\implies CD=\sqrt{(5+3)^2+(6-1)^2}
\\\\\\
CD=\sqrt{8^2+5^2}\implies CD=\sqrt{64+25}\implies CD=\sqrt{89}[/tex]
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points }\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&F&(~ -6 &,& 4~)
% (c,d)
&G&(~ 8 &,& -2~)
\end{array}\qquad
% coordinates of midpoint
\left(\cfrac{ x_2 + x_1}{2}\quad ,\quad \cfrac{ y_2 + y_1}{2} \right)
\\\\\\
\left( \cfrac{8-6}{2}~~,~~\cfrac{-2+4}{2} \right)\implies \left( \cfrac{2}{2}~~,~~\cfrac{2}{2} \right)\implies (1,1)[/tex]
[tex]\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ -2 &,& -3~)
% (c,d)
&&(~ 1 &,& 1~)
\end{array}
\\\\\\
% slope = m
slope = m\implies
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-(-3)}{1-(-2)}\implies \cfrac{1+3}{1+2}\implies \cfrac{4}{3}[/tex]
