Answer: The coordinates of point S is (14,-10).
Step-by-step explanation:
Midpoint of line joining [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by :-
[tex](x,y)=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]
Given, The coordinates of point T are (0,2). The midpoint of ST is (7, -4).
Let (a,b) be the coordinates of point S.
Then,
[tex](7,-4)=(\dfrac{0+a}{2},\dfrac{2+b}{2})\\\\\Rightarrow\ 7=\dfrac{a}{2},\ \ \ -4=\dfrac{2+b}{2}\\\\\Rightarrow\ a=7\times 2= 14, \ \ 2+b= 2\times-4 =-8\\\\\Rightarrow\ a=14,\ \ \ 2+b=-8\\\\\Rightarrow\ a=14, \ b= -8-2=6--10\\\\\Rightarrow\ a=14,\ b=-10[/tex]
Hence, the coordinates of point S is (14,-10).
