Given a tetrahedron (a,b,c,d) and any two distinct points let mx,y be the middle of the edge (x,y).Prove that the bary center go f the weighted points is the common section of the line segments...

Given a tetrahedron (a,b,c,d) and any two distinct points

let mx,y be the middle of the edge (x,y).Prove that the bary center go f the weighted points

is the common section of the line segments (ma,b,mc,d), (ma,c,mb,d), and (ma,d,mb,c). Show that if gd is the bary center of the weighted points

then g is the bary center of

and