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NDA 2 2024 Maths, question 56

Topic: Analytical geometry

Q56

The diagonals of a quadrilateral ABCDABCD are along the lines x−2y=1x-2y=1 and 4x+2y=34x+2y=3. The quadrilateral ABCDABCD may be a

  1. (a) rectangle
  2. (b) cyclic quadrilateral
  3. (c) parallelogram
  4. (d) rhombusCorrect answer

Solution.

Answer: (d) rhombus

  1. The diagonals have slopes 12\frac{1}{2} and −2-2, whose product is −1-1, so they are perpendicular.
  2. A rhombus is the quadrilateral known for perpendicular diagonals.
  3. A rectangle, a cyclic quadrilateral or a parallelogram does not in general have perpendicular diagonals.

Trap: A square also has perpendicular diagonals and is a rectangle too; the rhombus is the general shape that this property points to.