Question

Point G is the centroid of Δ ABC.

If l(BG) = 6 then l(BQ) = ______.

Answer 1

If l(BG) = 6 then l(BQ) = 9.

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 BG : GQ = 2 : 1

⇒ `("BG")/("GQ") = 2/1`

⇒ `("BG")/("BQ" - "BG") = 2/1`

⇒ `(6)/("BQ" - 6) = 2`

⇒ BQ − 6 = 3

⇒ BQ = 9