Question

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 :

• A. √2
• B. 2
• C. 2√2
• D. 4

Answer 1

Answer: (A)

√2

Answer 2

The correct answer is (C) : $2\sqrt2$
AB = x – 2y + 1 = 0
AC = 2x – y - 1 = 0
So A(1, 1)

Fig. Triangle

Altitude from B is BH $= x + 2y – 7 = 0 ⇒ B (3, 2)$
Altitude from C is CH $= 2x + y – 7 = 0 ⇒ C (2, 3)$
Centroid of ΔABC = E(2, 2) OE = $2\sqrt2$