JEE Main 2022 Mathematics question

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 orthocentre is (7/3, 7/3) is :

(1)
(2)2
(3)Correct
(4)4

Answer: (3)

Solution

The two given sides meet at A(1, 1). The altitude from B is perpendicular to AC (slope 2): through the orthocentre (7/3, 7/3), x + 2y − 7 = 0, and it meets AB (x − 2y + 1 = 0) at B(3, 2). The

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Question ID VK-035238