Straight Lines and Pair of Straight Lines Part 1

A ray of light passing through the point P(2,3) reflects on the x-axis at point A and the reflected ray passes through the point Q(5,4). Let R be the point that divides the line segment AQ internally into the ratio 2:1. Let the co-ordinates of the foot of the perpendicular M from R on the bisector of the angle PAQ be (α,β). Then, the value of 7α+3β is equal to