 The locations of points relative to a triangle with vertices "A", "B", and "C" and sides "AB", "BC", and "CA" are often expressed in extended ratio form as "triangular coordinates".In barycentric coordinates, a point with coordinates "α, β, γ" is the point upon which a weightless sheet of metal in the shape and size of the triangle would exactly balance if weights were put on the vertices, with the ratio of the weights at "A" and "B" being "α" ∶ "β", the ratio of the weights at "B" and "C" being "β" ∶ "γ", and therefore the ratio of weights at "A" and "C" being "α" ∶ "γ".In trilinear coordinates, a point with coordinates "x"