Certainly! Let's solve the problem step-by-step.
We are given the point [tex]\( P = (5, -2) \)[/tex].
We need to reflect this point over the x-axis. Reflecting a point over the x-axis involves changing the sign of its y-coordinate while keeping the x-coordinate the same.
1. The original coordinates of the point [tex]\( P \)[/tex] are [tex]\( (5, -2) \)[/tex].
2. To reflect over the x-axis, we retain the x-coordinate:
[tex]\[
x = 5
\][/tex]
3. We change the sign of the y-coordinate:
[tex]\[
y = -(-2) = 2
\][/tex]
So, after reflecting the point [tex]\( P = (5, -2) \)[/tex] over the x-axis, the new coordinates, [tex]\( R_{x \text{-axis}}(P) \)[/tex], are:
[tex]\[
(5, 2)
\][/tex]
