Question

Where would the barycenter of these two bodies be located given their masses?

Answer 1

It's kinda tough, since we don't know the actual numerical locations of the points, only an approximate picture.

The big ball has 11 times the mass of the small ball, so the small ball is 11 times as far from the barycenter as the big ball is.

If any of the points is marked at the actual barycenter, it can only be point-A .