Question

Find the coordinates of the foot of the perpendicular drawn from the point (1,2) to the line 3x+y+1=0

Answer 1

first calculate the slope line 3x+y+1=0
which is equal to m1= -3
let the slope of perpendicular line be m2
since both lines are perpendicular
therefore, m1 x m2 = -1
m2 = 1/3
since you got the slope of perpendicular line and you have a point on perpendicular
find its eqn by slope point form
since both lines are intersecting at foot of perpendicular
therefore the eqn of both lines must be equal for that point solve both the eqn by elimination method and you will get x and y which is required answer