Q27 of 30 Page 10

A ray of light passing through the point (1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A.


Let the coordinate of point A be (a, 0)


Draw a line (AL) perpendicular to the x –axis.


We know that angle of incidence is equal to angle of reflection. Hence, let


∠BAL =∠CAL = ɸ


Let ∠CAX = Ɵ


Therefore,


∠OAB = 1800 –(Ɵ+2ɸ) = 1800 –[Ɵ+2(900 - Ɵ)]


= 1800 – Ɵ+1800 +2Ɵ


= Ɵ


Thus, ∠BAX = 1800 – Ɵ


Now, slope of line AC =


------------ (1)


Slope of line AB =




----------------- (2)


From equations (1) and (2), we get,



⇒ 3a – 3 = 10 – 2a


⇒ a =


Therefore, the coordinates of point A are .

More from this chapter

All 30 →
25

Two lines passing through the point (2, 3) intersects each other at an angle of 60o. If slope of one line is 2, find equation of the other line.

 26

A person standing at the junction (crossing) of two straight paths represented by the equations 2x – 3y + 4 = 0 and 3x + 4y – 5 = 0 wants to reach the path whose equation is 6x – 7y + 8 = 0 in the least time. Find equation of the path that he should follow.

 28

Find equation of the line which is equidistant from parallel lines 9x + 6y – 7 = 0 and 3x + 2y + 6 = 0.

 29

If sum of the perpendicular distances of a variable point P (x, y) from the lines x + y – 5 = 0 and 3x – 2y +7 = 0 is always 10. Show that P must move on a line.