To find the reflection of a point across the x-axis, we follow a simple rule: the x-coordinate remains unchanged, while the y-coordinate changes to its negative value.
Given the point [tex]\( P = (4, -1) \)[/tex], here are the detailed steps to find its reflection across the x-axis:
1. Identify the Coordinates:
- The x-coordinate of point [tex]\( P \)[/tex] is 4.
- The y-coordinate of point [tex]\( P \)[/tex] is -1.
2. Change the y-coordinate:
- To reflect the point across the x-axis, we keep the x-coordinate the same.
- We change the y-coordinate to its negative. The negative of -1 is 1.
3. Form the New Coordinates:
- The x-coordinate remains 4.
- The new y-coordinate is 1.
Therefore, the reflection of the point [tex]\( P = (4, -1) \)[/tex] across the x-axis is [tex]\( R_{x-\text{axis}}(P) = (4, 1) \)[/tex].
