To reflect a point across the x-axis, we change the sign of its y-coordinate, while keeping the x-coordinate the same.

Given point $A(4, 1)$:

• The x-coordinate stays the same: $x = 4$.
• The y-coordinate changes sign: $y = -1$.

Thus, the reflection of point $A(4, 1)$ across the x-axis is $(4, -1)$.

So, the correct answer is D: (4, -1).

Would you like more details on this, or have any questions? Here are some related questions to explore:

1. What is the reflection of point $(x, y)$ across the y-axis?
2. How do you reflect a point across the origin?
3. How would you reflect a point across the line $y = x$?
4. What is the geometric significance of reflecting a point?
5. How do transformations such as translations and reflections differ?

Tip: Reflections only change one coordinate—across the x-axis, you change the y-value; across the y-axis, you change the x-value.