Question

in \\( \triangle pqr \\), point \\( c \\) is the centroid. if \\( pc = 9 \\), then \\( py = \\)
a 4.5
b 9
c 13.5
d 18

Explanation:

Step1: Recall centroid property

The centroid of a triangle divides each median in a ratio of \(2:1\). That is, if \(C\) is the centroid of \(\triangle PQR\) and \(PY\) is a median, then \(PC=\frac{2}{3}PY\).

Step2: Solve for \(PY\)

Given \(PC = 9\), from \(PC=\frac{2}{3}PY\), we can rewrite the formula to solve for \(PY\) as \(PY=\frac{3}{2}PC\).
Substitute \(PC = 9\) into the formula: \(PY=\frac{3}{2}\times9=\frac{27}{2}=13.5\).

Answer:

\(13.5\) (Option C)