Question

Point G is the centroid of Δ ABC.

If l(AP) = 6 then l(AG) = ______ and l(GP) = ______.

Answer 1

If l(AP) = 6 then l(AG) = 4 and l(GP) = 2.

Explanation:

In ∆ABC, the medians AP, BQ and CR to the sides BC, CA and AB respectively intersect at G. Since, centroid of a triangle divides the medians in the ratio of 2 : 1, then AG : GP = BG : GQ = CG : GR = 2 : 1.

We have, AG : GP = 2 : 1

⇒ ${\displaystyle \frac{\text{AG}}{\text{GP}}=\frac{2}{1}}$

⇒ ${\displaystyle \frac{\text{AG}}{\text{AP}-\text{AG}}=2}$

⇒ ${\displaystyle \frac{\text{AG}}{6-\text{AG}}}$ = 2

⇒ 2(6 − AG) = AG

⇒ 12 − 2AG = AG

⇒ 3AG = 12

⇒ ${\displaystyle \text{AG}=\frac{12}{3}}$

⇒ AG = 4