Answer:
G = (2, -1)
Step-by-step explanation:
You want ...
FG/FH = 1/6 = (G -F)/(H -F)
H -F = 6(G -F)
H +5F = 6G . . . . . . add 6F, simplify
G = (H +5F)/6 . . . . .divide by 6
Substituting the given coordinates, we get ...
G = ((-8, 19) +5(4, -5))/6 = (-8+20, 19 -25)/6 = (12, -6)/6
G = (2, -1)
