<P> In barycentric coordinates, a point with coordinates α: β: γ (\ displaystyle \ alpha: \ beta: \ gamma) 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, (\ displaystyle \ alpha: \ beta,) the ratio of the weights at B and C being β: γ, (\ displaystyle \ beta: \ gamma,) and therefore the ratio of weights at A and C being α: γ . (\ displaystyle \ alpha: \ gamma .) </P> <P> In trilinear coordinates, a point with coordinates x: y: z has perpendicular distances to side BC (across from vertex A) and side CA (across from vertex B) in the ratio x: y, distances to side CA and side AB (across from C) in the ratio y: z, and therefore distances to sides BC and AB in the ratio x: z . </P> <P> Since all information is expressed in terms of ratios (the individual numbers denoted by α, β, γ, (\ displaystyle \ alpha, \ beta, \ gamma,) x, y, and z have no meaning by themselves), a triangle analysis using barycentric or trilinear coordinates applies regardless of the size of the triangle . </P>

When is a slope ratio more than 1 when is it less than 1