Question

Find the other endpoint of the line segment with the given endpoint and midpoint. Endpoint 1: (−5,2) Midpoint: (2,−5) Endpoint 2=

Answer 1

`~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-5}~,~\stackrel{y_1}{2})\qquad (\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 +2}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M}}{(2~~,~~-5)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -5}{2}=2\implies x-5=4\implies \boxed{x=9} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +2}{2}=-5\implies y+2=-10\implies \boxed{y=-12}`