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`

Explanation

To find the locus of the vertex \( C \) of triangle \( ABC \) given that the centroid moves along the line \( 2x + 3y = 1 \), we will follow these steps:

### Step 1: Identify the coordinates of points A and B
Let the coordinates of point \( A \) be \( A(2, -3) \) and point \( B \) be \( B(-2, 1) \).

### Step 2: Assume the coordinates of point C
Let the coordinates of point \( C \) be \( C(h, k) \).

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