Let A($-$1, 1), B(3, 4) and C(2, 0) be given three points. A line y = mx, m > 0, intersects lines AC and BC at point P and Q respectively. Let A₁ and A₂ be the areas of $\Delta$ABC and $\Delta$PQC respectively, such that A₁ = 3A₂, then the value of m is equal to :