Question

If the foot of the perpendicular from the origin to a straight line is at the point (3, -4), then the equation of the line is:
1. 4x - 3y + 25 = 0
2. 4x + 3y - 25 = 0
3. 3x - 4y = 25
4. 3x - 4y + 25 = 0
5.

Answer 1

Correct Answer - Option 3 : 3x - 4y = 25

Concept: 

1. Equation of line of slope m passing through (x₁, y₁) is given by

(y - y₁) = m(x - x₁)

2. If two line with slope m₁ and m₂ are perpendicular to each other, then m₁m₂ = -1

Calculation:

Slope of line passes through (0, 0) and (3, -4) is 

\(m_1\ =\ \frac{-4\ -\ 0}{3\ -\ 0}\ =\ \frac{-4}{3}\)

Let slope of perpendicular at (3, -4) is m₂, then

m₁m₂ = -1 ⇒ m₂ = 3/4

We know that, 

Equation of line of slope m passing through (x1, y1) is given by

(y - y1) = m(x - x1)

Hence, equation of line passing through (3, -4) and slope 3/4 is given by

\((y\ +\ 4)\ =\ \frac{3}{4}(x\ -\ 3)\)

⇒ 3x - 4y = 25

Hence, option 3 is correct.