Let A(2, -3) and B(-2, 1) be two vertices of triangle ABC. If the centroid of triangle ABC moves along the line 2x + 3y = 1, find the locus of the vertex C.

2x + 3y = 9
2x - 3y = 7
3x + 2y = 5
3x - 2y = 3

Correct answer: 2x + 3y = 9

Solution

Centroid lies on 2x + 3y = 1, so 2*(h/3) + 3*((k-2)/3) = 1, giving 2h + 3k - 6 = 3, i.e., 2h + 3k = 9. Replacing h with x and k with y: locus is 2x + 3y = 9.

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