If the image of the point (2, 1) with respect to a line mirror is (5, 2), find the equation of the mirror.

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).


Also, let M be the midpoint of AB.


Coordinates of M



Diagram:



Let CD be the mirror.


Line AB is perpendicular to the mirror CD.


Slope of AB × Slope of CD = 1


Slope of CD = -1


Slope of CD = -3


Equation of the mirror CD



2y – 3 = -6 x + 21


6x + 2y – 24 = 0


3x + y -12 = 0


Hence, the equation of mirror is 3x + y -12 = 0


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