Find position of center of mass of four particles system, which are at vertices of a parallelogram as shown in figure. 
 

 

$x_{cm}=\frac{m_1{x}_1+m_2{x}_2+m_3{x}_3+m_4{x}_4}{m_1+m_2+m_3+m_4}$    ,  $y_{cm}=\frac{m_1{y}_1+m_2{y}_2+m_3{y}_3+m_4{y}_4}{m_1+m_2+m_3+m_4}$
$x_{cm}=\frac{m\left(0\right)+m\left(a\right)+m(a+b\cos \theta )+m\left(b\cos \theta \right)}{4m}$      ,  $y_{cm}=\frac{m\left(0\right)+m\left(0\right)+m\left(b\sin \theta \right)+m\left(b\sin \theta \right)}{4m}$
$x_{cm}=\left(\frac{a+b\cos \theta }{2}\right) , y_{cm}=\frac{b\sin \theta }{2}$