Question

N(3, – 4) is the foot of the perpendicular drawn from the origin to line L. Find the equation of line L.

Answer 1

Slope of ON = -4-0/3-0 = -4/3

Since line L ⊥ ON, 

slope of the line L is 3/4 and it passes through point N (3, 4).

Equation of the line in slope point form is y – y₁ = m(x – x₁)

Equation of line L is y-(-4) = 3/4 (x-3)

∴ 4(y + 4) = 3(x – 3) 

∴ 4y + 16 = 3x – 9 

∴ 3x – 4y – 25 = 0