1. **State the problem:** Reflect the point $(2,0)$ across the line $y=x$. 2. **Formula and rule:** When reflecting a point $(a,b)$ across the line $y=x$, the coordinates swap places. The reflected point becomes $(b,a)$. 3. **Apply the rule:** For the point $(2,0)$, swapping coordinates gives $(0,2)$. 4. **Final answer:** The reflection of $(2,0)$ across $y=x$ is $(0,2)$.