Given: Point (4,1) , line 3x – 4y + k = 0 and length of perpendicular is 2 units

To find: The values of k

Formula used:

We know that the length of the perpendicular from (m,n) to the line ax + by + c = 0 is given by,

D

The equation of the line is 3x – 4y + k =0

Here m= 4 and n= 1 , a = 3 , b = -4 , c = k and D=2 units

D

D

. or

or

or

The values of k are 2 and -18