Coordinates of centre of mass

Let us consider a system of  two particles m1 and m2 and placed at A and B having position coordinates x1 and x2 respectively from the origin as shown in above figure. If  Xcm is position coordinate of the centre of mass from origin
              Then d1=Xcm-x1
                       d2=x2-Xcm
                       d=x2-x1
         According to the definition of the centre of mass of the particles, if the centre of mass is defined  at C along AB  such that 
       product of (m1,AC)= product of (m2,CB)
       product of (m1,d1)= product of (m2,d2)
                Then
                   m1(Xcm-x1)=m2(x2-Xcm)
                    Xcm(m1+m2)=m1x1+m2x2
                     Xcm=(m1x1+m2x2)/(m1+m2)
        This is the position coordinate of the centre of mass.
From the above equation, the position coordinate is analog to the weighted mean displacement, i.e., where weighting factor for each particle is the fraction of the total mass that each particle has.
               Suppose, x1=0 and x2=d, then
                     Xcm=m2d/(m1+m2). This is the result when the origin is shifted to x1
               Suppose, x2=0 and x1=d, then
                          Xcm=m1d/(m1+m2). This is the result when the origin is shifted to x2
            If the origin is shifted to centre of mass i.e., Xcm=0 then x1=-d1 and x2=d2 then  
                    0=(-m1d1+m2d2)/(m1+m2) or m1d1=m2d2
                        Therefore, (d1/d2)=(m2/m1)
                 So, we can say that the ratio of the distances of centre of  mass  from masses is inverse ratio of their masses. We can say that the centre of mass is nearer to the heavier mass. The location of the centre of mass is independent of  the reference frame used to locate it. The centre of mass depends upon the masses the particles and the position of the particles relative to one another.