Prove that $pTq \longleftrightarrow |p| = |q|$ is Equivalence Relation on $A$ set of all point in the plane I want to prove that this relation is equivalence relation on A


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*$A$ set of all points in the plane

*$pTq \longleftrightarrow |p| = |q|$ , |p| is the distance from origin.


about transitivity,  there are counter-examples?
for reflexivity is obvious, $(x,x)$ the distance will be the same.
for symmetry $(x,y)\in R , (y,x) \in R$ the distances are the same.
if its Equivalence Relation what are the equivalence classes? and partition set?

I would like to get some suggestions.

Notice that this relation $T$ is defined by  the equality relation which's the most natural equivalence relation so $T$ will inherit the same properties and then it's also an equivalence relation.
Remark You can use this method for all relation defined by
$$xRy\iff f(x)=f(y)$$
For the class equivalence of $x$:
$$[x]=\{y;\, xRy\}=\{y;\, |x|=|y|\}=C(O,|x|) $$
where $C(O,|x|)$ is the circle of center the origin of the plane and radius $|x|$.
