Question

The reflection of the point (4, – 13) about the line 5x + y + 6 = 0 is ______.

विकल्प

• (– 1, – 14)

• (3, 4)

• (0, 0)

• (1, 2)

Answer 1

The reflection of the point (4, – 13) about the line 5x + y + 6 = 0 is (– 1, – 14).

Explanation:

Let (h, k) be the point of reflection of the given point (4, – 13) about the line 5x + y + 6 = 0.

The mid-point of the line segment joining points (h, k) and (4, – 13) is given by

`(h + 4)/2, (k - 13)/2`   (Why?)

This point lies on the given line, so we have

`5 (h + 4)/2 + (k - 13)/2 + 6` = 0

or 5 h + k + 19 = 0   .....(1)

Again the slope of the line joining points (h, k) and (4, –13) is given by `(k + 13)/(h - 4)`.

This line is perpendicular to the given line

Hence `(-5) (k + 3)/(h - 4)` = –1  (why?)

This gives 5k + 65 = h – 4

or h – 5k – 69 = 0   ....(2)

On solving (1) and (2)

We get h = –1 and k = –14.

Thus the point (–1, – 14) is the reflection of the given point.