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

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).

Also, let M be the midpoint of AB.

Coordinates of M  Diagram: Let CD be the mirror.

Line AB is perpendicular to the mirror CD.

Slope of AB × Slope of CD = 1 Slope of CD = -1

Slope of CD = -3

Equation of the mirror CD 2y – 3 = -6 x + 21

6x + 2y – 24 = 0

3x + y -12 = 0

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

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