Question

The line 4x − 3y + 12 = 0 meets the 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 point A (the point on the x-axis), the value of y = 0.

4x – 3y + 12 = 0

`=>` 4x = –12

`=>` 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

`y = 4/3x + 4`

Slope of this line = `4/3`

∴ Slope of a line perpendicular to the given line

= `(-1)/(4/3)`

= `(-3)/4`

The required equation of the line passing through A is:

y − y₁ = m(x − x₁)

`y - 0 = (-3)/4 (x + 3)`

4y = −3x − 9

3x + 4y + 9 = 0