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 – 9 – 16 = 0

∴ 3x – 4y – 25 = 0

∴ 3x – 4y = 25