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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.

Tracy found the length of GF Her work is shown below 16 22x 16 4x x 4 84 32 GF 232 GF 64 What error did Tracy make She used AG 2EG but the correct statement is class=

Respuesta :

bugglovedot

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

calculista

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

[tex]AG=2GE[/tex] ------> equation A

we have

[tex]AG=16\ GE=2x[/tex]

substitute in the equation A and solve for x

[tex]16=2*(2x)[/tex]

[tex]16=4x[/tex]

[tex]x=4[/tex]

[tex]BG=2GF[/tex] ------> equation B

we have

[tex]BG=8x[/tex]

substitute in the equation B and solve for GF

[tex]8x=2GF[/tex]

[tex]GF=4x[/tex]

substitute the value of x

[tex]GF=4*4=16[/tex]

therefore

the answer is

She used [tex]GF=2BG[/tex], but the correct statement is [tex]BG=2GF[/tex]

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