# Find the image of the point (3, 8) with respect to the line x + 3y = 7 assuming the line to be a plane mirror.

Given: (3, 8) is given point and line mirror is x + 3y – 7 = 0.

To find:

Image of point with respect to mirror line.

Explanation:

Let the image of A (3,8) be B (a,b).

Also, let M be the midpoint of AB.

Coordinates of M

Diagram:

Point M lies on the line x + 3y = 7

a + 3b + 13 = 0 … (1)

Lines CD and AB are perpendicular

Slope of AB × Slope of CD = 1

b – 8 = 3a – 9

3a-b-1 = 0 … (2)

Solving (1) and (2) by cross multiplication, we get:

a = -1, b = -4

Hence, the image of the point (3, 8) with respect to the line mirror x + 3y = 7 is

( 1, 4).

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