Sidon set in $\mathbb F_q\times\mathbb F_q$, where $q$ is the power of a odd prime

Question

I can't prove that the set $A=\{(r(x), s(x))\mid x\in\mathbb F_q\}$ is a Sidon set in $\mathbb F_q\times \mathbb F_q$, where $r(x)$ and $s(x)$ are two polynomials of degree $2$ or less in $\mathbb F_q[X]$ linearly independent. Anyone can helpme with some hints I would appreciete a lot. Thanks. Just to remember a Sidon set is set where all the sums between two elements are different, i.e., for all $a,b,c,d$ elements in a Sidon set, then $a+b\neq c+d$