Question

GH has a midpoint at M(7, 8.5). Point G is at (13, 17). Find the coordinates of point H.

Answer 1

`~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ G(\stackrel{x_1}{13}~,~\stackrel{y_1}{17})\qquad H(\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 +13}{2}~~~ ,~~~ \cfrac{ y +17}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M} }{(7~~,~~8.5)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +13 }{2}=7\implies x+13=14\implies \boxed{x=1} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +17 }{2}=8.5\implies y+17=17\implies \boxed{y=0}`