Q56 / 120 · NDA 2024 (Phase 2) · Mathematics

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

  • A
    rectangle
  • B
    cyclic quadrilateral
  • C
    parallelogram
  • Correct answer
    D
    rhombus

Solution

The Slope of the diagonal along the line $x-2 y=1$ is $\mathrm{m}_1=\frac{1}{2}$ and the slope of the diagonal along the line $4 x+2 y=3$ is $\mathrm{m}_2=-2$ Now, $\mathrm{m}_1 \mathrm{~m}_2=\frac{1}{2}(-2)=-1 \Rightarrow \mathrm{~m}_1 \mathrm{~m}_2=-1$ So, Diagonals are perpendicular to each others. $\Rightarrow$ The quadrilateral ABCD is a rhombus.

Hence, the correct answer is option: 'D'.

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