Q. 183.9( 31 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 :

The equation of the given line is


x +3y = 7


Let point B (a, b) be the image of point A (3, 8)


So, line (1) is the perpendicular bisector of AB.



Slope of AB = , while the slope of the line (1) =


Since, line (1) is perpendicular to AB.




=> b – 8 = 3a – 9


=> 3a – b = 1 --------------- (2)


Mid – point of AB =


The mid – point of line segment AB will also satisfy line (1).


Thus, from equation (1), we get,



a + 3 + 3b + 24 = 14


a + 3b = -13 -------------(3)


On solving equations (2) and (3), we get, a = -1 and b = -4


Therefore, the image of the given point with respect to the given line is (-1, -4).


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