Question

1. in △tuv, y is the centroid. if yw = 30, what is ty?

45
30
60
15

Explanation:

Step1: Recall centroid property

The centroid of a triangle divides each median in a 2:1 ratio. In \(\triangle TUV\), if \(Y\) is the centroid and \(TW\) is a median, then \(TY = 2YW\).

Step2: Given \(YW = 30\)

Since \(TY=2YW\), then \(TY = 2\times30=60\). And \(TV=TY + YV\), but in terms of the centroid - median relationship for this part of the problem, we are mainly focused on the ratio for the segment from the vertex to the centroid. Here we want to find \(TY\) which is 60.

Answer:

60