Two points P and Q in a plane are related if OP = OQ, where O is a fixed point. This relation is 

$$\begin{gathered} \mathrm{OP}=\mathrm{OP}\text{, the relation is reflexive } \\ \mathrm{OP}=\mathrm{OQ}\text{ then }\mathrm{OQ}=\mathrm{OP}\text{ also } \\ \text{ Therefore if }\mathrm{P}\text{ is related to }Q\text{ then }Q\text{ is related to }P\text{ also } \\ \text{ Hence relation is symmetric } \\ \text{ Let }P\text{ be related to }Q\text{ and }Q\text{ be related to }R \\ \Rightarrow \mathrm{OP}=\mathrm{OQ}\text{ and }\mathrm{OQ}=\mathrm{OR} \\ \Rightarrow \mathrm{OP}=\mathrm{OR},\mathrm{P}\text{ is related to }\mathrm{R} \end{gathered}$$
Hence Relation is equivalence relation.