Question

The midpoint of AB is M(1, 3). If the coordinates of A are (-1,5), what

are the coordinates of B?

Answer 1

`~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-1}~,~\stackrel{y_1}{5})\qquad B(\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 -1}{2}~~~ ,~~~ \cfrac{ y +5}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M} }{(1~~,~~3)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -1 }{2}=1\implies x-1=2\implies \boxed{x=3} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +5 }{2}=3\implies y+5=6\implies \boxed{y=1}`