Let `A(2,-3)a n dB(-2,1)` be vertices of a triangle `A B Cdot` If the centroid of this triangle moves on the line `2x+3y=1,` then the locus of the vertex `C` is the line `2x+3y=9` `2x-3y=7` `3x+2y=5` `3x-2y=3`

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`