Three particles of masses $1 \mathrm{kg}$, $\frac{3}{2} \mathrm{kg}$,  and $2 \mathrm{kg}$ are located at the vertices of an equilateral triangle of side $a$. The $x, y$coordinates of the centre of mass are

 Let the masses $1 \mathrm{kg}$, $\frac{3}{2} \mathrm{kg}$ and  $2 \mathrm{kg}$ are located at the vertices $A, B$and $C$ as shown in figure. The coordinates of points $A, B$ and $C$ are $(0,0),(a, 0)$ and $\frac{a}{2}$, $\frac{\sqrt{3}a}{2}$ respectively. The coordinates of centre of mass are  $X_{\mathrm{CM}}=\frac{m_1{x}_1+m_2{x}_2+m_3{x}_3}{m_1+m_2+m_3}$

$$\begin{gathered} =\frac{\left[1\times 0+\frac{3}{2}\times a+2\times \frac{a}{2}\right]}{\left[1+\frac{3}{2}+2\right]}=\frac{5a}{9} \\ {Y}_{\mathrm{CM}}=\frac{m_1{y}_1+m_2{y}_2+m_3{y}_3}{m_1+m_2+m_3} \end{gathered}$$

$=\frac{\left[1\times 0+\frac{3}{2}\times 0+2\times \frac{\sqrt{3}a}{2}\right]}{\left[1+\frac{3}{2}+2\right]}=\frac{2\sqrt{3}a}{9}=\frac{2a}{3\sqrt{3}}$