The points (-a,-b), (0,0), (a,b) and (a^{2}, ab) are:

Explanation

Let P(-a,-b), Q(0,0), R(a,b), and S(a^2,ab) be the points. Calculating the slopes between consecutive points: m_{PQ} = \frac{0 - (-b)}{0 - (-a)} = \frac{b}{a}, m_{QR} = \frac{b-0}{a-0} = \frac{b}{a}, and m_{RS} = \frac{ab-b}{a^2-a} = \frac{b(a-1)}{a(a-1)} = \frac{b}{a}. Since all segment slopes are equal and they share connecting points, all four points are collinear.

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