Question

Find the distance of the point (4, 1) from the line 3x – 4y + 12 = 0.

Answer 1

The length of perpendicular from a point (x₁, y₁) to the line ax + by + c = 0 is d = `|(ax_1 + by_1 + c)/(sqrt(a^2 + b^2))|`

∴ The distance of the point (4, 1) to the line 3x – 4y + 12 = 0 is

d = `|(3(4) - 4(1) + 12)/(sqrt(3^2 + (- 4)^2))|`

`= |(12 - 4 + 12)/(sqrt(9 + 16))|`

`= |20/5|`

= 4 units