Q. 125.0( 2 Votes )

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

Answer :

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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