Let A (2,-3) and B(-2,1) be vertices of a triangle ABC. If the centroid of this triangle moves on 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`