I have difficulty understanding a passage about the zeta function of a variety over $\mathbb{F}_p$. Here $X$ is a closed set of an $n$-dimensional affine space over a field $k$ of characteristic $p$, $\phi$ is the Frobenius map that takes a point $(a_1,...,a_n)$ to $(a_1^p,...,a_n^p)$.
if $x\in X$ is a point whose coordinates are in $\mathbb{F}_{p^r}$ and generate this field, then $X$ contains all the points $\phi^i(x)$ for $i=1,...,r$, and these are all distinct. We call a set $\xi=\{\phi^i(x)\}$ of this form a cycle, and the number $r$ of points of $\xi$ the degree of $\xi$. Now we can group together all the $\nu_r$ points $x\in X$ with coordinates in $\mathbb{F}_{p^r}$ into cycles. The coordinates of any of these points generate some subfield $\mathbb{F}_{p^d}\subset \mathbb{F}_{p^r}$, and it is known that $d|r$. We get a formula $$\nu_r=\sum\limits_{d|r}d\mu_d$$ where $\mu_d$ is the number of cycles of degree $d$.
My questions
1, Why are $\phi^i(x)$ for $i=1,...,r$ all distinct?
2, Why are the cycles disjoint?