Question

The points (-a, -b), (0, 0), (a, b) and ($a^2$, ab) are

• A. Collinear
• B. Vertices of a rectangle
• C. Vertices of a parallelogram
• D. None of these

Answer 1

The correct option is A

Collinear

Here area of quadrilateral is equal to $areaof△ABD$ + $areaof△BCD$

= $\left|\begin{array}{ccc}-a& -b& 1\\ 0& 0& 1\\ a^2& ab& 1\end{array}\right|$ + $\left|\begin{array}{ccc}0& 0& 1\\ a& b& 1\\ a^2& ab& 1\end{array}\right|$ = 0

Hence the points are collinear.