A ray of light passing through the point (1, 2) reflects on the x-axis at point A and the reflected - Maths - Straight Lines

Question

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

Gopal Mohanty · Accepted Answer

Let the coordinates 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 = Φ

Let ∠CAX = θ

∴∠OAB = 180° – (θ + 2Φ) = 180° – [θ + 2(90° – θ)]

= 180° – θ – 180° + 2θ

= θ

∴∠BAX = 180° – θ

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

Thus, the coordinates of point A are.

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

Thus, the coordinates of point A are

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.