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 \(( \bar { x } , \bar { y } )\).
Show that \(\bar { x } = \frac { 2 + 12 k } { 9 }\)
The centre of mass of the three particles lies at a point on the straight line with equation \(x + 2 y = 3\)