Find the distance of the point (2, 3) from the line 2x – 3y + 9 = 0 measured along a line making an angle of 45° with the x–axis.

Question

Philoid · Accepted Answer

Given: (x₁,y₁) = A(2, 3), θ = 45°

To find:

Distance of point from line.

Explanation:

So, the equation of the line is

Formula Used:

⇒

⇒ x – y + 1 = 0

Let PQ = r

Then, the coordinate of Q are given by

⇒ x, y

The coordinate of point Q is

Clearly, Q lies on the line 2x – 3y + 9 = 0

⇒

⇒ r = 4√2

Hence, the distance of the point from the given line is 4√2.