The distance of the origin from the centroid of the triangle whose two sides have the equations x - 2 y + 1 = 0 and 2 x - y - 1 = 0 and whose orthocenter is 7 3 , 7 3 is:

Step-by-step solution

Let A B ≡ x - 2 y + 1 = 0 and A C ≡ 2 x - y - 1 = 0 So, A 1 ,   1 Now, altitude from B which is perpendicular to line 2 x - y - 1 = 0 and which passes through 7 3 , 7 3 is B H = x + 2 y - 7 = 0 , Now intersection of B H   &   A B will give point B 3 ,   2 Similarly, altitude from C is C H = 2 x + y - 7 = 0 ⇒ C 2 ,   3 Centroid of △ A B C = E 2 ,   2   &   O E = 2 2 where O is origin.