Question

A ray of light coming from the point (1, 2) is reflected at a
point A on the x-axis and then passes through the point (5,
3). The coordinates of the point A are
(a) (13/5,0)
(b) (5/13,0)
(c)(-7,0)
(d) none of these

Answer 1

Answer:

Let coordinates A( x , 0 )

By law of reflection angles

a = b or

a + angle QAX = b +angle QAX

Or slopes equal

$\frac{2 - 0}{1 - x} = \frac{3 - 0}{5 - x} \\ 3(x - 1) = 2(x - 5) \\ x = - 7$