Greetings,

If a relation is defined on the Cartesian plane $\displaystyle \mathbb{R} \times \mathbb{R}$ by $\displaystyle (x_1,y_1) \; \backsim \; (x_2,y_2) \; \Longleftrightarrow \; (x_2,y_2) \; = \; (rx_1,ry_1)$ for some $\displaystyle r \; > \; 0$, what would the equivalence classes be? This seems like it should be easy, but I'm drawing a blank on it for whatever reason so for any help I would be grateful.