Q191 / 270 · NDA 2017 (Phase 2) · Mathematics

The points $(\mathrm{a}, \mathrm{b}),(0,0),(-a,-b)$ and $\left(a b, b^2\right)$ are

  • A
    the vertices of a parallelogram
  • B
    the vertices of a rectangle
  • C
    the vertices of a square
  • Correct answer
    D
    collinear

Solution

Given points, $\mathrm{A}(\mathrm{a}, \mathrm{b}), \mathrm{B}(0,0), \mathrm{C}(-\mathrm{a},-\mathrm{b}), \mathrm{D}\left(\mathrm{ab}, \mathrm{b}^2\right)$. Slope of $A B=\frac{b-0}{a-0}=\frac{b}{a}$ Slope of $B C=\frac{b}{a}$ Slope of $A C=\frac{b}{a}$ Slope of $B D=\frac{b}{a}$. So, the points are collinear

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

Relevant Questions