Question

Find the coordinates of the missing endpoint if M is the midpoint of XY.

Answer 1

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ X(\stackrel{x_1}{-11}~,~\stackrel{y_1}{-6})\qquad Y(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{x-11}{2}~~,~~\cfrac{y-6}{2} \right)=\stackrel{\stackrel{Midpoint}{M}}{(15,4)}\implies \begin{cases} \cfrac{x-11}{2}=15\\[0.8em] x-11=30\\ \boxed{x=41}\\[-0.5em] \hrulefill\\ \cfrac{y-6}{2}=4\\[0.8em] y-6=8\\ \boxed{y=14} \end{cases}$

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ X(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad Y(\stackrel{x_2}{19}~,~\stackrel{y_2}{0}) \\\\\\ \left( \cfrac{19+x}{2}~~,~~\cfrac{0+y}{2} \right)=\stackrel{\stackrel{Midpoint}{M}}{(-4,8)}\implies \begin{cases} \cfrac{19+x}{2}=-4\\[0.8em] 19+x=-8\\ \boxed{x=-27}\\[-0.5em] \hrulefill\\ \cfrac{0+y}{2}=8\\[0.8em] \boxed{y=16} \end{cases}$