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JEE Main202523 Jan 2025Morning ShiftMathematicsStraight LinesActual

Let the area of a P Q R with vertices P(5,4), Q(-2,4) and R(a, b) be 35 square units. If its orthocenter and centroid are O (2, 14 5 ) and C(c, d) respectively, then c+2 d is equal to

Options

  1. A8 3
  2. B7 3
  3. C2
  4. D3

Correct answer

D. 3

Step-by-step solution

aligned & Equation of lines Q R=5 x+2 y+2=0 & Equation of lines P R=10 x-3 y-38=0 & Point R(2,-6) & Centroid = ( 5-2+2 3 , 4+4-6 3 ) & = ( 5 3 , 2 3 ) & c+2 d= 5 3 + 4 3 =3 aligned

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