Question

Point M is the midpoint of AC , find the coordinates of the missing endpoint when you are given one endpoint, and the coordinates of the midpoint. M(-1,5) and A(-4,3)

Answer 1

`~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{3})\qquad C(\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 +3}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M}}{(-1~~,~~5)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -4}{2}=-1\implies x-4=-2\implies \boxed{x=2} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +3}{2}=5\implies y+3=10\implies \boxed{y=7}`