Question

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

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 $BG=2GF$