Question

1. point o is a centroid of the triangle lmn. if om = 38 cm, what is mp?

Explanation:

Step1: Recall centroid property

The centroid of a triangle divides each median into a ratio of \(2:1\), where the segment from the vertex to the centroid is twice the segment from the centroid to the midpoint. So, \(OM:OP = 2:1\), and \(MP=OM + OP\). Let \(OP=x\), then \(OM = 2x\). Given \(OM = 30\) cm, so \(2x=30\), then \(x = 15\) cm.

Step2: Calculate MP

\(MP=OM + OP=30 + 15 = 45\) cm.

Answer:

\(45\) cm