Question

tracys work

1. 16 = 2(2x)
2. 16 = 4x; x = 4
3. 8(4) = 32
4. gf = 2(32)
5. gf = 64

tracy found the length of gf.
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 found that gf = 64, but the correct value of gf is 8.
she used gf = 2bg, but the correct statement is bg = 2gf.

Explanation:

Step1: Recall the centroid property

In a triangle, the centroid divides each median in a ratio of \(2:1\). That is, if a median is \(m\) and the centroid is \(G\), then \(BG = 2GF\) (where \(B\) is a vertex and \(F\) is the mid - point of the opposite side).

Step2: Analyze Tracy's work

Tracy wrote \(GF = 2BG\) in step 4. According to the centroid theorem, the correct relationship is \(BG=2GF\).

Answer:

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