# Find the image of the point (2, 1) with respect to the line mirror x + y – 5 = 0.

Given: (2,1) is given point and line mirror is x + y – 5 = 0

To find:

Image of the point with respect to mirror line.

Explanation:

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

Let M be the midpoint of AB.

Coordinates of M are

Diagram:

The point M lies on the line x + y 5 = 0

a + b = 7 … (1)

Now, the lines x + y 5 = 0 and AB are perpendicular.

Slope of AB × Slope of CD = 1

a – 2 = b – 1 ……(2)

Adding eq (1) and eq (2):

2a = 8

a = 4

Now, from equation (1):

4 + b = 7

b = 3

Hence, the image of the point (2, 1) with respect to the line mirror x + y 5 = 0 is (4, 3).

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