Answer:
see below
Explanation:
Put the (x, y) values of point F into the equation for line AG and see if they work:
y = (b/(a+c))x
For (x, y) = (a+c, b), this is ...
b = (b/(a+c))(a+c) = b·(a+c)/(a+c) = b·1 = b . . . . . a true statement
Yes, F lies on line AG.