The relation R on the set A of points in a plane, given by R- {(P, Q); Distance of the point P from the origin is same as the distance of Q from the origin } is

Equivalence

for every point p ∈ plane

distance (p from origin is same) ⇒ every $(P, P) ∈ R$ (Reflexive)

if $(P, Q) ∈ R$

distance of P form O ⇒ $(Q, P) ∈ R$ (Symmetric)

= distance of Q from O 

$(P, Q) ∈ R, (Q, S) ∈ R$

⇒ distance of P form O = distance of Q from O = distance of S from O

$⇒ (P, S) ∈ R$ (Transitive)

⇒ R → equivalence relation