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JEE Main202522 Jan 2025Morning ShiftMathematicsStraight LinesActual

Let the triangle PQR be the image of the triangle with vertices (1,3),(3,1) and (2,4) in the line x+2 y=2 . If the centroid of PQR is the point ( , ) , then 15( - ) is equal to :

Options

  1. A19
  2. B24
  3. C21
  4. D22

Correct answer

D. 22

Step-by-step solution

The centroid G^ ( , ) of P Q R be image of centroid of given triangle P^ Q^ R^ . Centroid of P^ Q^ R^ = ( 1+3+2 3 , 3+1+4 3 )=G^ (2, 8 3 ) . Image of G (2, 8 3 ) , w.r.t. line x+2 y=2 is ( , ) Then -2 1 = - 8 3 2 = -2 (2+ 16 3 -2 ) 1+4 -2 1 = - 8 3 2 =- 32 15 =- 2 15 and =- 8 5 Then 15( - )=15 (- 2 15 + 24 15 )=22

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