Question

AB is the line segment, M is the midpoint of AB. A is (-4,5) and M is (5, -1), what are the coordinates of B?

Answer 1

`~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-4}~,~\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 -4}{2}~~~ ,~~~ \cfrac{ y +5}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M} }{(5~~,~~-1)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -4 }{2}=5\implies x-4=10\implies \boxed{x=14} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +5 }{2}=-1\implies y+5=-2\implies \boxed{y=-7}`