Question

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 ____.

Answer 1

Correct answer is 31

By observation we see that A (α, 0).

And β = y -cordinate of R

Now P’ is image of P in y = 0 which will be P ' (2,-3)