Question

tracy found the length of $overline{gf}$. her work is shown below. what error did tracy make? 1. $16 = 2(2x)$ 2. $16 = 4x; x = 4$ 3. $8(4)=32$ 4. $gf = 2(32)$ 5. $gf = 64$ 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.

Explanation:

Step1: Recall centroid property

In a triangle, the centroid divides each median in a 2:1 ratio. The longer - part is towards the vertex. So if \(G\) is the centroid and \(BF\) is a median, then \(BG = 2GF\).

Step2: Analyze Tracy's work

Tracy used \(GF = 2BG\) which is incorrect.

Answer:

She used \(GF = 2BG\), but the correct statement is \(BG=2GF\).