Question 129
A beetle is creeping on the coordinate plane, starting from point $(0; -1)$, along a straight line until reaching the $x$-axis at point $(-x; 0)$ where $x$ is a positive real number. After that it turns $90^\circ$ to the right and creeps again along a straight line until reaching the $y$-axis. Then it again turns right by $90^\circ$ and creeps along a straight line until reaching the $x$-axis, where it once more turns right by $90^\circ$ and creeps along a straight line until reaching the $y$-axis.
a) Can it happen that both the length of the beetle's journey and the distance between its initial and final point are rational numbers?
b) Can it happen that both the length of the beetle's journey and the distance between its initial and final point are integers?
a) Can it happen that both the length of the beetle's journey and the distance between its initial and final point are rational numbers?
b) Can it happen that both the length of the beetle's journey and the distance between its initial and final point are integers?