Respuesta :
Answer: (-2,2)
Step-by-step explanation:
The coordinates of the point P(x,y) which divides the line segment joining M(a,b) and N (c,d) in ratio m:n is given by :-
[tex]x=\dfrac{mc+na}{m+n},\ y=\dfrac{md+nb}{m+n}[/tex]
Given : Line segment DE has endpoints D(-4, -2) and E(1, 8).
Let (x,y) be the coordinates of point F which divides line segment DE in ratio 2:3.
Then , the coordinates of the point F(x,y) will be :-
[tex]x=\dfrac{2(1)+3(-4)}{2+3},\ y=\dfrac{2(8)+3(-2)}{2+3}\\\\\Rightarrow\ x=-2,\ y=2[/tex]
Hence, the coordinates of F = (-2,2)