# NCERT Class 11 Mathematics Solutions: Chapter 10 – Straight Lines Miscellaneous Exercise 10 Part 12 (For CBSE, ICSE, IAS, NET, NRA 2022)

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1. A ray of light passing through the point reflects on the axis at point and the reflected ray passes through the point . Find the coordinates of .

Answer: Find Point A

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

Consider

Now, slope of line

… eq (1)

Slope of line

… eq (2)

From equations (1) and (2) ,

So, the coordinates of point are

2. Prove that the product of the lengths of the perpendiculars drawn from the points

and to the line is .

Answer:

The equation of the given line is

… eq (1)

Length of the perpendicular from point to line (1) is

… eq (2)

Length of the perpendicular from point to line (2) is

… eq (3)

On multiplying equations (2) and (3) ,

[]

So, proved.