Question

Which is the other endpoint of a line segment with one endpoint at (-2,-5) and midpoint at (3,2)

Answer 1

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{x-2}{2}~~,~~\cfrac{y-5}{2} \right)~=~\stackrel{midpoint}{(3,2)}\implies \begin{cases} \cfrac{x-2}{2}=3\\[1em] x-2=6\\ \boxed{x=8}\\[-0.5em] \hrulefill\\ \cfrac{y-5}{2}=2\\[1em] y-5=4\\ \boxed{y=9} \end{cases}$