Question

Find the distance of the point A(– 2, 3) from the line 12x – 5y – 13 = 0.

Answer 1

Let p be the perpendicular distance of the point A(– 2, 3) from the line 12x – 5y – 13 = 0
Here, a = 12, b = – 5, c = – 13, x₁ = – 2, y₁ = 3

∴ p = `|("a"x_1 + "b"y_1 + "c")/sqrt("a"^2 + "b"^2)|`

= `|(12(-2) - 5(3) - 13)/sqrt(12^2 + (-5)^2)|`

= `|(-24 - 15 - 13)/sqrt(144 + 25)|`

= `|(-52)/13|`

= 4 units.