Question

D is the midpoint of CE. E has coordinates (5,-10), and D has

coordinates (11,4). Find the coordinates of C.

Answer 1

`~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ C(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad E(\stackrel{x_2}{5}~,~\stackrel{y_2}{-10}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 5 +x}{2}~~~ ,~~~ \cfrac{ -10 +y}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE D} }{(11~~,~~4)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ 5 +x }{2}=11\implies 5+x=22\implies \boxed{x=17} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ -10 +y }{2}=4\implies -10+y=8\implies \boxed{y=18}`