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

Answer: (A)

The point $O(0,0)$ is the midpoint of $A(-a,-b)$ and $B(a,b)$.
$\therefore A$, $O$, $B$ are collinear and equation of $AO$ is $y=\frac{b}{a}x$
$D=\left(a^2,ab\right)$ satisfies the equation of $AO$
$\therefore$ The four points are collinear.