Question

The line 4x − 3y + 12 = 0 meets x-axis at A. Write the co-ordinates of A. Determine the equation of the line through A and perpendicular to 4x – 3y + 12 = 0.

Answer 1

For the point A (the point on x-axis), the value of y = 0.

4x – 3y + 12 = 0

${\displaystyle \Rightarrow }$ 4x = –12

${\displaystyle \Rightarrow }$ x = –3

Co-ordinates of point A are (–3, 0)

Here, (x₁, y₁) = (–3, 0)

The given line is 4x – 3y + 12 = 0

3y = 4x + 12

${\displaystyle y=\frac{4}{3}x+4}$

Slope of this line = ${\displaystyle \frac{4}{3}}$

∴ Slope of a line perpendicular to the given line

= ${\displaystyle \frac{-1}{\frac{4}{3}}}$

= ${\displaystyle \frac{-3}{4}}$

Required equation of the line passing through A is

y − y₁ = m(x − x₁)

${\displaystyle y-0=\frac{-3}{4}(x+3)}$

4y = −3x − 9

3x + 4y + 9 = 0