The distance of the line x+y-8=0 from (4, 1) measured along the direction whose slope is -2, is

The equation of a line passing through P(4,1) and slope -2 isx−415=y−125 ∵tan⁡θ=−2⇒cos⁡θ=−15,sin⁡θ=25Suppose it cuts x+y-B=0 at Q such that PQ=r. Then, the coordinates of Q are given by x−4−15=y−12=r⇒x=4−r5,y=1+2r5Since Q lies on the line x+y-B=0. ∴ 4−r5+1+2r5−8=0⇒r=35Hence, required distance =35 units.