Question

The coordinates of the midpoint of segment GH are M (4,3) and the coordinates of one endpoint are G (5,-6)

Answer 1

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ G(\stackrel{x_1}{5}~,~\stackrel{y_1}{-6})\qquad H(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{x+5}{2}~~,~~\cfrac{y-6}{2} \right)~~=~~\stackrel{\stackrel{midpoint}{M}}{(4,3)}\implies \begin{cases} \cfrac{x+5}{2}=4\\[1em] x+5=8\\ \boxed{x=3}\\ \cline{1-1} \cfrac{y-6}{2}=3\\[1em] y-6=6\\ \boxed{y=12} \end{cases}$