Three particles of masses $$\(2 m, 3 m\)$$ and $$\(4 m\)$$ are placed at the points with coordinates $$\((-2,5),(2,-3)\)$$ and $$\((3 k, k)\)$$ respectively, where $$\(k\)$$ is a constant. The centre of mass of the three particles is at the point $$\((\bar{x}, \bar{y})\)$$. (a) Show that $$\(\bar{x}=\frac{2+12 k}{9}\)$$ (2) The centre of mass of the three particles lies at a point on the straight line with equation $$\(x+2 y=3\)$$ (b) Find the value of $$\(k\)$$. (4)

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