Question

The coordinates of point T are (0,4). The midpoint of ST is (4,-6). What are the coordinates of S

Answer 1

`~~~~~~~~~~~~\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{\textit{\large Midpoint} }{(4~~,~~-6)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ 0 + x }{2}=4\implies \boxed{x=8} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ 4 + y }{2}=-6\implies 4+y=-12\implies \boxed{y=-16}`