Question

The coordinates of point T are (0,4). The midpoint of Line ST is (2,-5). Find Coordinates of aS

Answer 1

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ S(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad T(\stackrel{x_2}{0}~,~\stackrel{y_2}{4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{0+x}{2}~~,~~\cfrac{4+y}{2} \right)~~=~~\stackrel{midpoint}{(2~,~-5)}\implies \begin{cases} \cfrac{0+x}{2}=2\\[1em] \boxed{x=4}\\ \cline{1-1} \cfrac{4+y}{2}=-5\\[1em] 4+y=-10\\ \boxed{y=-14} \end{cases}$