Question

Given the midpoint and one endpoint of a line segment, find the other endpoint.

Answer 1

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points }\\ \quad \\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~{{ -9}} &,&{{ -1}}~) % (c,d) &&(~{{ x}} &,&{{ y}}~) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)$

$\bf \left( \cfrac{x-9}{2}~~,~~\cfrac{y-1}{2} \right)=\stackrel{midpoint}{(8~~,~~14)}\implies \begin{cases} \cfrac{x-9}{2}=8\\\\ x-9=16\\ \boxed{x=25}\\ -------\\ \cfrac{y-1}{2}=14\\\\ y-1=28\\ \boxed{y=29} \end{cases}$

Answer 2

Given the midpoint and one endpoint of a line segment, find the other endpoint.
Endpoint: (-9, -1), midpoint: (8, 14)