(n-1) equal point masses each of mass m are placed

Given,

$r_{c m}=\frac{(n-1) m b+m a}{(n-1) m+m}$

Where,

rcm is the place where mass m is placed at the nth vertex

rcm = 0

$\frac{(n-1) m b+m a}{(n-1) m+m}=0$

(n-1)mb + ma = 0

b = -ma/(n-1)m

$\vec{b}=-\frac{\vec{a}}{n-1}$

Where,

$\vec{b}$ is the position vector. Also, the negative sign indicates that the centre of mass lies on the other side of the nth vertex.