The barycentric coordinates should be just (x,y,1-x-y) should they not?
Given a planar triangle defined by vertices p1 = (1,0), p2 = (0,1), and p3 = (0,0), and an arbitrary point p = (x,y), specify the barycentric coordinates b1, b2, and b3 in terms of x and y. Im not quite understand this question.