Question

In ΔPQR, point C is the centroid. If PC = 9, then PY =
A) 4.5
B) 9
C) 13.5
D) 18

Answer 1

centroid divides median into the ratio 2:1 then

PC/CY=9/x=2/1

x=4.5

then the total length PY = 9+4.5=13.5

Answer 2

Therefore the value of $PY$ is $13.5$

Step-by-step explanation:

Given;

For a $\bigtriangleup PQR$, point $C$ is the centroid and $PC=9$

The medians of a triangle intersect at a point called centroid that is two third of the distance from each vertex to the to the mid point of the opposite side.

By this theorem;

  $\frac{PC}{PY}=\frac{2}{3}$

⇒$PY=\frac{3}{2}PC$

⇒$PY=\frac{3}{2}\times 9$

∴$PY=\frac{27}{2}=13.5$

So the value of $PY$ is $13.5$