Geometric meaning of reflexive and symmetric relations A relation $R$ on the set of real numbers can be thought of as a subset of the $xy$ plane. Moreover an equivalence relation on $S$ is determined by the subset $R$ of the set $S \times S$ consisting of those ordered pairs $(a,b)$ such that $ a \sim b$. 
With this notation explain the geometric meaning of the reflexive and symmetric properties.
Since reflexivity implies the presence of all ordered pairs of the type $(a,a)$, may be the geometric meaning is the straight line passing through $(0,0)$ and $(a,a)$ which is nothing but the line $y=x$.
For symmetric presence of $(a,b)$ implies the presence of $(b,a)$. Is its geometric meaning the straight line joining $(a,b)$ and $(b,a)$??
Thanks for the help!!

Your description of reflexivity is correct.
For symmetry it means that the subset $R$ is "symmetric" around the line $y = x$, this means that for any point $(a, b)\in R$ its mirror point $(b, a)\in R$ (it's the point you get by doing reflection in the line $y=x$), i.e. either none of the two points $(a, b)$ and $(b, a)$ is included in $R$, or both of them are included in $R$.
Thus the "graph" of $R$ is the same as its mirror image when doing reflection in $y=x$.
