Answer: The midpoint of the line ST is (4,2) .
Step-by-step explanation:
The midpoint (x,y) of any line joining (a,b) and (c,d) is given by :-
[tex](x,y)=(\dfrac{a+c}{2}, \dfrac{b+d}{2})[/tex]
The given coordinate-points : S= (−2, 8) and T=(10, −4)
Let (x,y) be the midpoint of the line ST.
Then , the midpoint of the line ST would be
[tex](x,y)=(\dfrac{-2+10}{2}, \dfrac{8+(-4)}{2})[/tex]
[tex]\Rightarrow\ (x,y)=(\dfrac{8}{2}, \dfrac{8-4}{2})[/tex] [∵ (-)(+)=(-)]
[tex]\Rightarrow\ (x,y)=(4, \dfrac{4}{2})[/tex]
[tex]\Rightarrow\ (x,y)=(4, 2)[/tex]
Hence, the midpoint of the line ST = (4,2)
