Given :  The image of a point (1,5) when reflected in a line LM is (9,5).

To find : equation of the line LM.

Solution:

The image of a point (1,5) when reflected in a line LM is (9,5)

Line joining ( 1 , 5)  & ( 9 , 5) slope

= ( 5 - 5)/(9 - 1)

= 0/8

= 0

Hence Slope of LM = (-1/0)

Mid point of  ( 1 , 5)  & ( 9 , 5)  = ( 1 + 9)/2 , ( 5 + 5)/2

= 5 , 5

Point will lie on LM

y - 5  = (1/0) (x - 5)

=> 0(y - 5) = x - 5

=> 0 = x - 5

=> x = 5

equation of the line LM.   is  x = 5

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