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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?

 

 Dec 25, 2020
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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

 

 

cool cool cool

 Dec 25, 2020
edited by CPhill  Dec 25, 2020

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