Question

(c) Find the co-ordinate of the foot of the
perpendicular from the points (-1, 3) to the line 3x – 4y - 16 = 0.​

Answer 1

let (a,b) be the coordinates

slope of line joining (-1,3)&(a,b) is m1=b-3/a+1

slope of line 3x-4y-16=0 or 3/4x-4, m2=3/4

since these 2 lines are perpendicular,m1m2=-1

{b-3/a+1}.{3/4}=-1

3b-9/4a+4=-1

3b-9=4a-4

4a+3b=5...(1)

point(a,b) lies on line 3x-4y=16

3a-4b=16...(2)

solve 1 &2

a=68/25. b=-49/25

ans=68/25,49/25