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JEE Main 2025 Jan 23 Shift 1, Mathematics Q13: Solution of Triangles

JEE Main2025Jan 23, Shift 1Mathematics
Q.

Let the area of a with vertices , and be 35 square units. If its orthocentre and centroid are and respectively, then is equal to

  1. A

  2. B

  3. C

  4. D

Solution

$ \text{Equation of line }QR:\;5x+2y+2=0 $

$ \text{Equation of line }PR:\;10x-3y-38=0 $

$ \therefore R(2,-6) $

$ \text{Centroid} = \left( \dfrac{5-2+2}{3}, \dfrac{4+4-6}{3} \right) $

$ = \left( \dfrac{5}{3}, \dfrac{2}{3} \right) $

$ c+2d = \dfrac{5}{3} +\dfrac{4}{3} =3 $

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