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JEE Main202529 Jan 2025Morning ShiftMathematicsStraight LinesActual

Let (A B C ) be a triangle formed by the lines (7 x-6 y+3=0, x+2 y-31=0 ) and (9 x-2 y-19=0 ). Let the point ((h, k) ) be the image of the centroid of ( A B C ) in the line (3 x+6 y-53=0 ). Then (h^2+k^2+h k ) is equal to:

Options

  1. A47
  2. B37
  3. C36
  4. D40

Correct answer

B. 37

Step-by-step solution

aligned centroid of ABC & = ( 9+3+5 3 , 11+4+13 3 ) & = ( 17 3 , 28 3 ) aligned Let image of centroid with respect to line mirror is aligned & ( h , k ) & ( k - 28 3 ~h - 17 3 ) (- 1 2 )=-1 & & 3 ( ~h + 17 3 2 )+6 ( k +28 3 2 )=53 aligned Solving (1) & (2) we get h =3, k =4 h ^2+ k ^2+ hk =37

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