Question

The midpoint of AB is M(1, 4). If the coordinates of A are (8, 7), what are the

coordinates of B?

Answer 1

`~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{8}~,~\stackrel{y_1}{7})\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 +8}{2}~~~ ,~~~ \cfrac{ y +7}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M}}{(1~~,~~4)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +8}{2}=1\implies x+8=2\implies \boxed{x=-6} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +7}{2}=4\implies y+7=8\implies \boxed{y=1}`