Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
The points $(a, b),(0,0),(-a,-b)$ and $\left(a b, b^{2}\right)$ are
MathematicsStraight LinesNDANDA 2017 (Phase 2)
Options:
  • A the vertices of a parallelogram
  • B the vertices of a rectangle
  • C the vertices of a square
  • D collinear
Solution:
2396 Upvotes Verified Answer
The correct answer is: the vertices of a rectangle
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 $\mathrm{BC}=\frac{\mathrm{b}}{\mathrm{a}}$
Slope of $A C=\frac{b}{a}$
Slope of $\mathrm{BD}=\frac{\mathrm{b}}{\mathrm{a}}$.
So. the points are collinear.

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.