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JEE Main202310 Apr 2023Evening ShiftMathematicsStraight LinesActual

Let the equations of two adjacent sides of a parallelogram A B C D be 2 x - 3 y = - 23 and 5 x + 4 y = 23 . If the equation of its one diagonal A C is 3 x + 7 y = 23 and the distance of A from the other diagonal is d , then 50 d 2 is equal to ______________

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Step-by-step solution

Given, The equations of two adjacent sides of a parallelogram A B C D be 2 x - 3 y = - 23 and 5 x + 4 y = 23 , So, A B ≡ 2 x - 3 y = - 23 and B C ≡ 5 x + 4 y = 23 Also given, A C ≡ 3 x + 7 y = 23 Solving the above lines we get, A ( – 4 ,   5 ) ,   B ( – 1 ,   7 ) ,   C ( 3 ,   2 ) We know that, Diagonal of parallelogram have same midpoint, So A C and B D have same mid-point and let point D be x , y , So midpoint formula we get, x - 1 2 = - 4 + 3 2 ⇒ x = 0

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