Question

The midpoint of cd is (8,-6). the coordinates of c are (0,-5). Find the coordinates of D

Answer 1

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ C(\stackrel{x_1}{0}~,~\stackrel{y_1}{-5})\qquad D(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{x+0}{2}~~,~~\cfrac{y-5}{2} \right)~~=~~\stackrel{midpoint}{(8~,~-6)}\implies \begin{cases} \cfrac{x+0}{2}=8\\[1em] \boxed{x = 16}\\ \cline{1-1} \cfrac{y-5}{2}=-6\\[1em] y-5=-12\\ \boxed{y=-7} \end{cases}$