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