Q. 135.0( 2 Votes )
If the image of the point (2, 1) with respect to the line mirror be (5, 2), find the equation of the mirror.
Answer :
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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