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

Options

A. 3x - 2y = 3
B. 2x - 3y = 7
C. 3x + 2y = 5
D. 2x + 3y = 9

Answer

D

Explanation

Let (h,k) be the coordinates of the third vertex C .
Then , the coordinates of the centroid G are
`G ((h + 2 - 2)/(3) , (k-3 +1)/(3)) -= G ((h)/(3) , (k-2)/(3))`
It lies on 2x + 3y = 1 .
`therefore (2h)/(3) + 3 ((k-2)/(3)) = 1`
`implies 2h + 3k - 6 = 3 implies 2h + 3k = 9`
Hence , the locus of G (h,k) is 2x + 3y = 9