We take for $\Omega$ (only in this question) the interior of the equilateral triangle with vertices $(1,0), (-1/2, \sqrt{3}/2)$ and $(-1/2, -\sqrt{3}/2)$. We define, for all $\lambda \in \mathbb{R}^*$ and all pairs $(x_0, y_0) \in \mathbb{R}^2$:
$$\Omega_{x_0, y_0, \lambda} = \left\{ \lambda(x,y) + (x_0, y_0) \mid (x,y) \in \Omega \right\}$$
Draw a figure on which both $\Omega$ and $\Omega_{2,1,1/2}$ appear.