Question

The midpoint of AB M (0,−2). If the coordinates of A are (5, -1), what are the coordinates of B

Answer 1

`~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{5}~,~\stackrel{y_1}{-1})\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 +5}{2}~~~ ,~~~ \cfrac{ y -1}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M} }{(0~~,~~-2)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +5 }{2}=0\implies x+5=0\implies \boxed{x=-5} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y -1 }{2}=-2\implies y-1=-4\implies \boxed{y=-3}`