Three particles having their masses in the ratio `1 : 3 : 5` are kept at the vertices of a triangle `ABC`. Coordinate of `A`, `B` and `C` are `(9,-3)`, `(3,4)` and `(0,0)`. Find the coordinates of the centre of mass.
Hint. `x_(cm)=(sum_(i-1)^(3)m_(i)x_(i))/(sum_(i=1)^(3)m_(i))`, `y_(cm)=(sum_(i=1)^(3)m_(i)y_(i))/(sum_(i=1)^(3)m_(i))`

Explanation

Let the masses be `m`, `3m` and `5m`
`x_(cm)=(9m+9m)/(9m)=(18m)/(9m)=2`
`y_(cm)=(-3m+12m)/(9m)=(9m)/(9m)=1`
Hence, the coordinates of the centre of mass are `(2,1)`.