A straight line drawn through the point A (2, 1) making an angle with positive x–axis intersects another line x + 2y + 1 = 0 in the point B. Find length AB.

Question

Philoid · Accepted Answer

Given: (x₁,y₁) = A(2, 1), θ = 45°

To find:

Length AB.

Explanation:

So, the equation of the line is

Formula Used:

⇒

⇒ x – y – 1 = 0

Let PQ = r

Then, the coordinate of Q is given by

⇒ x , y

The coordinate of point Q is

Clearly, Q lies on the line x + 2y + 1 = 0

⇒

⇒ r

Hence, the length of AB is