[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{3}~,~\stackrel{y_1}{5})\qquad N(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{x+3}{2}~~,~~\cfrac{y+5}{2} \right)=\stackrel{\stackrel{Mid point}{M}}{(6,2)}\implies \begin{cases} \cfrac{x+3}{2}=6\\[0.8em] x+3=12\\ \boxed{x=9}\\[-0.5em] \hrulefill\\ \cfrac{y+5}{2}=2\\[0.8em] y+5=4\\ \boxed{y=-1} \end{cases}[/tex]
if M is the midpoint it is the middle so to get N just do what you would to get from A to M. A is (3,5) and M is (6,2), to get from A to M you -3 from x-value and -3 from y-value. Do the same to the M coordinates to find N, 6-3=3, and 2-3=-1.The coordinates of N are (3,-1)
