Question

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

Answer 1

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 = \(\Big(\frac{3+a}{2},\frac{8+b}{2}\Big)\) 

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).