Question

find the co-ordinate on line x+y-4=0 whose distance from line 4x+3y=10 is 1

Answer 1

solve the two equations simultaneously
from this you will get the values of x and y hence coordinates are found ...pretty simple

Answer 2

let point be p=(h,k) lies on line x+y=4~y=4-x~k=4-h
given,distance from p to line 4x+3y==10 is 1
~(4h+3k-10)/5=1
~4h+3(4-h)-10=5 (or) 4h+3(4-h)-10=-5
~4h+12-3h-10=5(or) 4h+12-3h-10=-5
~h=3 (or) h=-7
~k=1(or)k=11
therefore the point is p=(3,1) (or)p=(-7,11)