To find the reflection of the point [tex]\( P = (4, -1) \)[/tex] over the x-axis, we follow these steps:
1. A point reflected over the x-axis changes the sign of its y-coordinate, while the x-coordinate remains the same.
2. Given point [tex]\( P = (4, -1) \)[/tex];
3. To reflect [tex]\( P \)[/tex] over the x-axis, we keep the x-coordinate as 4 and change the sign of the y-coordinate from -1 to 1.
Thus, the coordinates of the reflection [tex]\( R_{x \text{-axis}}(P) \)[/tex] are [tex]\( (4, 1) \)[/tex].
Therefore, [tex]\( R_{x \text{-axis}}(P) = (4, 1) \)[/tex].
