Question

The midpoint of CD is M(-1,-2). One endpoint is C (-9,-4). Find the coordinates of the other endpoint D.

Answer 1

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points }\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &C&(~ -9 &,& -4~) % (c,d) &D&(~ x &,& y~) \end{array}\qquad % coordinates of midpoint \left(\cfrac{ x_2 + x_1}{2}\quad ,\quad \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{x-9}{2}~~,~~\cfrac{y-4}{2} \right)=\stackrel{midpoint~M}{(-1~~,~~-2)}\implies \begin{cases} \cfrac{x-9}{2}=-1\\\\ x-9=-2\\ \boxed{x=7}\\ ----------\\ \cfrac{y-4}{2}=-2\\\\ y-4=-4\\ \boxed{y=0} \end{cases}$