1. **State the problem:** Find the intersection of the sets $\{2, 9\}$ and $\{1, 4, 9\}$. This means we want to find all elements that are in both sets. 2. **Recall the definition of intersection:** The intersection of two sets $A$ and $B$, denoted $A \cap B$, is the set of all elements that are members of both $A$ and $B$. 3. **Identify common elements:** Check each element of the first set $\{2, 9\}$ to see if it is also in the second set $\{1, 4, 9\}$. - $2$ is not in $\{1, 4, 9\}$. - $9$ is in $\{1, 4, 9\}$. 4. **Write the resulting set:** The intersection is $\{9\}$. 5. **Conclusion:** The correct answer is choice A: $\{2, 9\} \cap \{1, 4, 9\} = \{9\}$.