# NCERT Class 11 Mathematics Solutions: Chapter 10 –Straight Lines Miscellaneous Exercise 10 Part 12

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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 .

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 .

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.

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