ABCD is a square with side length 2. E is the midpoint of AB, F is the midpoint of AD, and 2CG = 3FG. What is the area of triangle EBG?
+128631 Let F =(0,1) C = (2,2)
And 2CG = 3 FG means that
FG / CG = 2/3
So....there are 5 parts of FC and FG is 2 of them....thus FG = (2/5)FC
We can find the coordinates of G thusly
[ 0 + (2/5) (2 -0) , 1 + (2/5)(2 - 1) ] = (4/5, 1 + 2/5 ) = (4/5, 7/5)
And 7/5 is the height of EGB and the base EB = 1
So [EGB ] =(1/2) (1) (7/5) = 7 /10
