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

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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