Question

the midpoint of kl is m(4.8, -7.8). one endpoint is l(0.6, -5.6). find the coordinates of the other endpoint k.

Answer 1

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points }\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &k&(~ x &,& y~) % (c,d) &l&(~ 0.6 &,& -5.6~) \end{array}\qquad % coordinates of midpoint \left(\cfrac{ x_2 + x_1}{2}\quad ,\quad \cfrac{ y_2 + y_1}{2} \right)$

$\bf \left( \cfrac{0.6+x}{2}~~,~~\cfrac{-5.6+y}{2} \right)~=~\stackrel{midpoint}{(4.8~,~-7.8)}\quad \begin{cases} \cfrac{0.6+x}{2}=4.8\\\\ 0.6+x=9.6\\ \boxed{x=9}\\ ---------\\ \cfrac{-5.6+y}{2}=-7.8\\\\ -5.6+y=-15.6\\ \boxed{y=10} \end{cases}$