Answer :

Given:


Line x + 3y – 7 = 0, point (3, 8).


To find:


The coordinates of the image.


Explanation:


Let the given point be A(3,8) and its image in the line x + 3y 7 = 0 is B(h,k).


The midpoint of AB is that lies on the line x + 3y 7 = 0.



h + 3k + 13 = 0 … (1)


AB and the line x + 3y 7 = 0 are perpendicular.


Slope of AB × Slope of the line = - 1



3h – k – 1 = 0 … (2)


Solving (1) and (2), we get:
(h, k) = (
1, 4)


Hence, the image of the point (3,8) in the line x + 3y 7 = 0 is ( 1, 4).


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