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JEE Main2014MathematicsStraight LinesActual

Given three points P , Q , R with P 5 , 3 and R lies on the x - axis. If the equation of R Q is x - 2 y = 2 and P Q is parallel to the x - axis, then the centroid of Δ P Q R lies on the line

Options

  1. Ax - 2 y + 1 = 0
  2. B2 x + y - 9 = 0
  3. C2 x - 5 y = 0
  4. D5 x - 2 y = 0

Correct answer

C. 2 x - 5 y = 0

Step-by-step solution

Given, P 5 , 3 and equation of R Q is x - 2 y = 2 ⇒   R ≡ 2 , 0 lies on x - axis and Q lies on a line parallel to x - axis through P which is y = 3 . Hence, on solving y = 3 and x - 2 y = 2 ⇒ x = 8 ∴    Q ≡ 8 , 3 Centroid ≡ 5 + 8 + 2 3 , 3 + 3 + 0 3 ≡ 5 , 2 ∵   x 1 + x 2 + x 3 3 , y 1 + y 2 + y 3 3 5 , 2 lies on   2 x - 5 y = 0

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