Q. 135.0( 2 Votes )

# If the image of the point (2, 1) with respect to the line mirror be (5, 2), find the equation of the mirror.

Answer :

__Given:__ image of (2,1) is (5,2)

__To find:__

The equation of the mirror.

Explanation:

Let the image of A (2, 1) be B (5, 2).

Let M be the midpoint of AB.

Coordinates of M

Diagram:

Let CD be the mirror.

The line AB is perpendicular to the mirror CD.

∴ Slope of AB × Slope of CD = − 1

⇒ Slope of CD = -3

Thus, the equation of the mirror CD is

⇒ 2y – 3 = -6x + 21

⇒ 6x + 2y -24 = 0

⇒ 3x + y – 12 = 0

Hence, the equation of mirror is 3x + y – 12 = 0.

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