Rational points of unipotent groups

Question

Let $G$ be an unipotent group (smooth unipotent group scheme) of finite type over $F_q$ then why the set of his rational points over $F_q$ is a finite group?

Answer 1

This is true for any algebraic variety (scheme of finite type) over $\mathbb F_q$, because the rational points are the solutions of some polynomial equations in $\mathbb F_q$ and that $\mathbb F_q$ is finite ! When the variety you start with is a group scheme, the set of the rational points form a group, this is essentially part of the definition.