Question

HELP ASAP!!!

M is the midpoint of AN, A has coordinates
(2, -3), and M has coordinates (5, 1). Find
the coordinates of N.

Answer 1

`~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\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 +2}{2}~~~ ,~~~ \cfrac{ y -3}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M} }{(5~~,~~1)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +2 }{2}=5\implies x+2=10\implies \boxed{x=8} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y -3 }{2}=1\implies y-3=2\implies \boxed{y=5}`