Let A` (2,-3)` and B `(-2,1) ` be the vertices of `Delta ABC`. If the centroid of this triangle moves on the line `2x+3y=1` then the locus of the vertex `C`is the line

Explanation

Let C be `(alpha,beta)`.
The centroid is
`((2-2+alpha)/(3),(-3+1+beta)/(3)),i.e.,((alpha)/(3),(beta-2)/(3))`
This lies on `2x+3y=1`. Therefore,we get
`2(alpha/(3))+3(beta-2/(3))=1`
or `2alpha+3beta=9`