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The points $$(a, 0)$$, $$(0, a)$$, $$(-a, 0)$$ and $$(0, -a)$$ are the vertices of a
The diagonals join $$(a, 0)$$ to $$(-a, 0)$$ and $$(0, a)$$ to $$(0, -a)$$. Both have length $$2|a|$$, bisect each other at the origin and lie along perpendicular axes. A quadrilateral whose diagonals are equal and are perpendicular bisectors of each other is a square, each side being $$\sqrt{2}\,|a|$$.
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