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JEE Main20211 Sep 2021Evening ShiftMathematicsStraight LinesActual

Let the points of intersections of the lines x - y + 1 = 0 , x - 2 y + 3 = 0 and 2 x - 5 y + 11 = 0 are the mid points of the sides of a triangle ABC . Then the area of the triangle ABC is

Correct answer

6

Step-by-step solution

If P ,   Q ,   R are mid-points of sides of ∆ A B C then 4 × A r e a ( ΔPQR ) = A r e a ( ∆ ABC ) Area of   Δ ABC = 4 × 1 2 a 1   b 1 c 1 a 2   b 2 c 2 a 3   b 3 c 3 2 C 1 C 2 C 3 Where C 1 , C 2 , C 3 are cofactors of   c 1 , c 2 , c 3   Δ ABC = 4 × 1 2 1 - 1 1 1 - 2 3 2 - 5 11 2 ( - 1 ) ( 3 ) ( - 1 ) = 2 × 9 ÷ 3 = 6

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