# A straight line, AB, undergoes two reflections. First reflection occurs in a mirror, placed in the vertical plane at x=0. The reflected line undergoes another reflection, in another mirror, placed in the horizontal plane at y=0. If the x and y intercepts of line AB are p and q respectively before the reflections, then the equation of the line after the second reflection will be:

1
by shalnusara

2015-11-03T21:15:52+05:30
The x and y intercepts of the unreflected ray are (p,0) and (0,q).
therefore the equation of the line(ray) before reflection is

(x/p) + (y/q) = 1
qx + py - pq = 0

now as the ray is getting reflected two times, first on the y-axis and then on the x-axis, the slope of the line remains unchanged.
therefore the equation of the line will become

qx + py + c = 0 where c is just a constant
now after the second reflection the x intercept of the line becomes (-p,0)
therefore
-pq + 0 + c = 0 therefore c = pq

therefore the equation of the second line becomes

qx + py + pq = 0