Question

The midpoint of AB is M(1,-4). If the coordinates of A are (-3, -6), what are

the coordinates of B?

Answer 1

`~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{-6})\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 -3}{2}~~~ ,~~~ \cfrac{ y -6}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M}}{(1~~,~~-4)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -3}{2}=1\implies x-3=2\implies \boxed{x=5} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y -6}{2}=-4\implies y-6=-8\implies \boxed{y=-2}`