Question

2 gr 1.3 △abc is shown with centroid point g. af = 21, ad = 8.5, dg = 4, and bf = 6.25. part a: what is the length of (overline{ag})? (ag=) part b: what is the length of (overline{bc})? (bc=)

Explanation:

Step1: Recall centroid property for \(AG\)

The centroid divides each median in a ratio of \(2:1\). For median \(AD\), \(AG = 2DG\). Given \(DG = 4\).
\(AG=2\times4\)

Step2: Recall centroid property for \(BC\)

The centroid is the intersection of medians. For median \(BF\), \(BF\) is half of \(BC\) (since \(F\) is the mid - point of \(AC\) and \(BF\) is a median). Given \(BF = 6.25\).
\(BC = 2BF\)

Answer:

• Part A: \(AG = 8\)
• Part B: \(BC=12.5\)