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 
. Then, the value of 
is equal to_______.
Text Solution
Verified by Experts31
(31)
By observation we see that A( 
,0).
And 
= y-cordinate of R
…(1)
Now P' is image of P in y = 0 which will be P'(2,-3)
Equation of P'Q is (y + 3) = 
i.e. 3y + 9 = 7x-14
by solving with y = 0
…(2)
By (1), (2)
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