Question

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

Options

• 4x + 3y = 0

• 3x – 4y – 25 = 0

• x – y – 7 = 0

• 4x – 3y – 24 = 0

Answer 1

N(3, – 4) is the foot of the perpendicular drawn from the origin to a line L. Then, the equation of the line L is 3x – 4y – 25 = 0.

Explanation:

Slope of line perpendicular to line L = `(-4 - 0)/(3 - 0) = (-4)/3`

Now, slope of line L = `(-1)/(((-4)/3)) = 3/4`

Now, required equation of line L is given by

`(y + 4) = 3/4 (x - 3)`

`\implies` 4y + 16 = 3x – 9

`\implies` 3x – 4y – 25 = 0