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JEE Main202127 Jul 2021Evening ShiftMathematicsStraight LinesActual

Two sides of a parallelogram are along the lines 4 x + 5 y = 0 and 7 x + 2 y = 0 . If the equation of one of the diagonals of the parallelogram is 11 x + 7 y = 9 , then other diagonal passes through the point:

Options

  1. A1 , 2
  2. B2 , 2
  3. C2 , 1
  4. D1 , 3

Correct answer

B. 2 , 2

Step-by-step solution

Both the lines 4 x + 5 y = 0 , 7 x + 2 y = 0 pass through origin. D is the point of intersection of 4 x + 5 y = 0   &   11 x + 7 y = 9 So upon solving we get the coordinates of point D = 5 3 , - 4 3 Also, point B is the point of intersection of 7 x + 2 y = 0   &   11 x + 7 y = 9 So, coordinates of point B = - 2 3 , 7 3 The diagonals of parallelogram bisect each other, so the mid point of B D is 5 3 - 2 3 2 , - 4 3 + 7 3 2 = 1 2 , 1 2 The equation of diagonal A C is y - 0 = 1 2 - 0 1 2 -

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