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JEE Main202624 January 2026Morning ShiftMathematicsStraight LinesActual

Let A (1,0), B (2,-1) and C ( 7 3 , 4 3 ) be three points. If the equation of the bisector of the angle ABC is x+ y=5 , then the value of ²+ ² is

Options

  1. A13
  2. B10
  3. C5
  4. D8

Correct answer

B. 10

Step-by-step solution

For angle bisector of angle ABC where A(1,0), B(2,-1), C( 7 3 , 4 3 ). Direction BA: (1-2, 0-(-1)) = (-1, 1) , unit vector (- 1 2 , 1 2 ) Direction BC: ( 1 3 , 7 3 ) , magnitude 5 2 3 , unit vector ( 1 5 2 , 7 5 2 ) Angle bisector direction (sum of unit vectors): ( -4 5 2 , 12 5 2 ) → direction (-1, 3) Normal to bisector: (3, 1) . Bisector passes through B(2, -1): 3(x-2) + 1(y+1) = 0 → 3x + y - 5 = 0 Therefore = 3 , = 1 , so ^2 + ^2 = 9 + 1 = 10

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