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 the x-axis), the value of y = 0.

4x - 3y + 12 = 0 $\Rightarrow$ 4x = -12 $\Rightarrow$ 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

y = + 4

Slope of this line =

Slope of a line perpendicular to the given line =

Required equation of the line passing through A is

y - y₁ = m(x - x₁)

y - 0 = (x + 3)

4y = -3x - 9

3x + 4y + 9 = 0