The coordinates of a triangle `ABC` are `A(1,2)`, `B(4,6)` and `C(-3,-2)`. Three particles of masses `1kg`, `2kg` and `m kg` are placed the vertices of the triangle. If the coordinate of the centre of mass are `((3)/(5),2)`, calculate the mass `m`.

Explanation

To solve the problem, we need to find the mass \( m \) of the third particle placed at vertex \( C \) of triangle \( ABC \) given the coordinates of the vertices and the center of mass.

### Step-by-Step Solution:

1. **Identify the Given Data**:
- Coordinates of points:
- \( A(1, 2) \)
- \( B(4, 6) \)
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