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1998

JEE Main 1998 Mathematics question on Straight Lines and Pair of Lines

The diagonals of a parallelogram PQRSPQRS are along the lines x+3y=4x + 3y = 4 and 6x−2y=76x - 2y = 7. Then, PQRSPQRS must be a
  1. A.
    rectangle
  2. B.
    square
  3. C.
    cyclic quadrilateral
  4. D.
    rhombus
Show answer and solution

Correct option: D

Solution

The two diagonal lines have slopes -1/3 and 3. Their product is (-1/3)(3) = -1, so the diagonals are perpendicular. In a parallelogram, perpendicular diagonals is the condition for a rhombus. (A rectangle requires equal diagonals, not perpendicular ones.) Hence PQRS must be a rhombus.

[1998]

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