If we have a point represented in barycentric notation , then how can we find its cartesian co-ordinates if the cartesian co -ordinates of the points relative to which the barycenter is calculated is known?

E.g for a triangle if we know the baryceter co-ordinates of a point(say P) and also the cartesian co-ordinates of all its vertices, then how do we find the cartesian co-ordinates of P?

Thanks.