Question

The coordinates of point T are ​(0​,3​).The midpoint of ST is ​(5​,-8​).Find the coordinates of point S.

Answer 1

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ S(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad T(\stackrel{x_2}{0}~,~\stackrel{y_2}{3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{0+x}{2}~~,~~\cfrac{3+y}{2} \right)=\stackrel{midpoint}{(5,-8)}\implies \begin{cases} \cfrac{0+x}{2}=5\\[0.8em] \boxed{x=10}\\[-0.5em] \hrulefill\\ \cfrac{3+y}{2}=-8\\[0.8em] 3+y=-16\\ \boxed{y=-19} \end{cases}$