When a point is reflected across the x-axis, the x-coordinate remains the same while the y-coordinate changes its sign.
Given the point \( A(4, -7) \):
- The x-coordinate is \( 4 \).
- The y-coordinate \( -7 \) changes to \( 7 \).
So, the coordinates of the reflected point \( A' \) are \( (4, 7) \).
Therefore, the coordinates of \( A' \) are \( (4, 7) \).