The distance of the origin from the centroid of the triangle whose two sides have the equations
x – 2y + 1 = 0 and 2x – y – 1 = 0 and whose orthocenter is (7/3, 7/3) is :
x – 2y + 1 = 0 and 2x – y – 1 = 0 and whose orthocenter is (7/3, 7/3) is :
- √2
- 2
- 2√2
- 4
The Correct Option is A
Solution and Explanation
The correct answer is (C) : \(2\sqrt2\)
AB = x – 2y + 1 = 0
AC = 2x – y - 1 = 0
So A(1, 1)
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 = \(2\sqrt2\)
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Concepts Used:
Coordinate Geometry
The central idea in coordinate geometry is to assign numerical coordinates to points in a plane or space, which allows us to describe their positions and relationships using algebraic equations. The most common coordinate system is the Cartesian coordinate system, named after the French mathematician and philosopher René Descartes.