Question

[Geometry Basics] I'm just checking if this is correct:

Answer 1

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ x &,& y~) % (c,d) &&(~ -9 &,& -1~) \end{array}\qquad % coordinates of midpoint \left(\cfrac{ x_2 + x_1}{2}\quad ,\quad \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{-9+x}{2}~~,~~\cfrac{-1+y}{2} \right)=\stackrel{midpoint}{(8,14)}\implies \begin{cases} \cfrac{-9+x}{2}=8\\\\ -9+x=16\\ \boxed{x=25}\\ -------\\ \cfrac{-1+y}{2} =14\\\\ -1+y=28\\ \boxed{y=29} \end{cases}$

$\bf -------------------------------\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ x &,& y~) % (c,d) &&(~10 &,& 12~) \end{array}\qquad \\\\\\ \left( \cfrac{10+x}{2}~~,~~\cfrac{12+y}{2} \right)=\stackrel{midpoint}{(6,9)}\implies \begin{cases} \cfrac{10+x}{2}=6\\\\ 10+x=12\\ \boxed{x=2}\\ -------\\ \cfrac{12+y}{2} =9\\\\ 12+y=18\\ \boxed{y=6} \end{cases}$