Show that the relation in the set of points in a plane given by : distance of the…

MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

11. Show that the relation

R

in the set

A

of points in a plane given by

\mathrm{R}=\{(\mathrm{P}, \mathrm{Q})

: distance of the point P from the origin is same as the distance of the point Q from the origin

\}

, is an equivalence relation. Further, show that the set of all points related to a point

\mathrm{P} \neq(0,0)

is the circle passing through P with origin as centre.