# Equivalence Classes in the cartesian plane

The relation $\sim$ on $R \times R$ is defined by $(a,b) \sim (c,d)$ iff $a^2 +b^2 = c^2 + d^2$.

I have already proven that this is an equivalence relation but I need to give a geometric description of the equivalence classes and I'm not sure how.

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## 2 Answers

Note that $x^2+y^2=r^2$

Two points are equivalent if they are equidistant from the origin

The equivalence classes are circles that have the origin as a center

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Hint: What does $x^2+y^2=r^2$ represent?

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