Properties of TriangleHard

Question

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

Options

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

Solution

If C be (h, k) then centroid is (h/3, (k - 2)/3) it lies on 2x + 3y = 1.
⇒   locus is 2x + 3y = 9.

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