# 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.

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

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