Question

The midpoint is AB is M (-1,0). If the coordinates are A are (6,-4), what are coordinates for B

Answer 1

`~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{6}~,~\stackrel{y_1}{-4})\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 +6}{2}~~~ ,~~~ \cfrac{ y -4}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M} }{(-1~~,~~0)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +6 }{2}=-1\implies x+6=-2\implies \boxed{x=-8} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y -4 }{2}=0\implies y-4=0\implies \boxed{y=4}`