The perpendicular distance from the point 1,1 to the line which is perpendicular to 4x−3y+1=0 and passing through 3,5 is

The equation of any line perpendicular to the line 4x−3y+1=0 can be taken as 3x+4y+k=0 It is passing through the point (3,5)It implies 33+45+k=09+20+k=0k=−29 Hence the equation of the line perpendicular to the line 4x−3y+1=0 and passing through  the point (3,5) is 3x+4y−29=0 The perpendicular distance from a point Px1,y1 to the line ax+by+c=0 is ax1+by1+ca2+b2 The perpendicular distance from a point (1,1) to the line 3x+4y−29=0 is 31+41−2916+9=225