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JEE Main20257 Apr 2025Morning ShiftMathematicsStraight LinesActual

Let ABC be the triangle such that the equations of lines A B and A C be 3 y-x=2 and x+y=2 , respectively, and the points B and C lie on x -axis. If P is the orthocentre of the triangle A B C , then the area of the triangle PBC is equal to

Options

  1. A4
  2. B10
  3. C8
  4. D6

Correct answer

D. 6

Step-by-step solution

aligned & Equation of Altitude AP : x =1 & Equation of Altitude BP : y -0=1( x +2) & x =1 & & x - y +2=0 & P (1,3) & Area of PBC = 1 2 4 3=6 aligned

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