Q. 205.0( 4 Votes )
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 :
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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