This ain't so tough!
Points on which are at unit distance from are:
A) (3,1) or (-7,1)
B) (3,1) or (-9,13)
C) (2,2) or (-8,12)
D) (-7,11) or (-17,21)
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1 solution
It is given that the points are at distance 1 from the line 4x+3y=0. It is also given,that the points lie on the line x+y=4. =>|(4x+3y)/5|=1....eqn.1 =>x+y=4 or 4x+4y=16. 4x=16-4y....eqn.2 Substituting 2 in 1, |(16-y)/5|=1. Either 16-y=5=>y=11 or 16-y=-5=>y=21. Substituting for both values in the equation 4x+3y=0, The points are (-7,11) or (-17,21)