Question

The midpoint of AB a is M. If A is at (-1,4) and M is at (7,-5) find the coordinates of B:

Answer 1

`~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-1}~,~\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 -1}{2}~~~ ,~~~ \cfrac{ y +4}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M} }{(7~~,~~-5)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -1 }{2}=7\implies x-1=14\implies \boxed{x=15} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +4 }{2}=-5\implies y+4=-10\implies \boxed{y=-14}`