Question

Tracy found the length of GF. Her work is shown below.

16 = 2(2x)
16 = 4x; x = 4
8(4) = 32
GF = 2(32)
GF = 64
What error did Tracy make?
She used AG = 2EG, but the correct statement is 2AG = GE.
She found that x = 4, but the correct value for x is 2.
She used GF = 2BG, but the correct statement is BG = 2GF.
She found that GF = 64, but the correct value of GF is 8.

Answer 1

she used GF=2BG,but the statement is correct BG=2GF

Answer 2

we know that

The centroid of a triangle is the intersection of the three medians of the triangle. The coordinates of the centroid are also two-thirds of the way from each vertex along that segment

so

in this problem

The point G is the centroid of the triangle ABC

`AG=2GE` ------> equation A

we have

`AG=16\ GE=2x`

substitute in the equation A and solve for x

`16=2*(2x)`

`16=4x`

`x=4`

`BG=2GF` ------> equation B

we have

`BG=8x`

substitute in the equation B and solve for GF

`8x=2GF`

`GF=4x`

substitute the value of x

`GF=4*4=16`

therefore

the answer is

She used
`GF=2BG`, but the correct statement is
`BG=2GF`