Find the distance of the point (2, 5) from the line 3x + y + 4 = 0 measured parallel to a line having slope 3/4.

Given: (x₁,y₁) = A(2, 5), tanθ

⇒ sin θ and cos θ

To find:

The distance of a point from the line parallel to another line.

Explanation:

So, the equation of the line passing through (2, 5) and having a slope is

Formula Used:

⇒

⇒ 3x – 4y + 14 = 0

Let 3x – 4y + 7 = 0 intersect the line 3x + y + 4 = 0 at point P.

Let AP = r

Then, the coordinate of P are given by

⇒ x and y

Thus, the coordinate of P is

Clearly, P lies on the line 3x + y + 4 = 0

⇒

⇒ 3r = – 15

⇒ r = – 5

Hence, the distance of the point (2, 5) from the line 3x + y + 4 = 0 is 5