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