To find the reflection of point [tex]\( P \)[/tex] across the x-axis, we need to apply the rules of reflection. Here’s how you can do that step-by-step:
1. Identify the coordinates of point [tex]\( P \)[/tex]:
Point [tex]\( P \)[/tex] is given as [tex]\( (-3, 4) \)[/tex].
2. Understand the reflection across the x-axis:
When reflecting a point across the x-axis, the x-coordinate remains the same, but the y-coordinate changes its sign. Hence, if the original point is [tex]\( (x, y) \)[/tex], the reflected point will be [tex]\( (x, -y) \)[/tex].
3. Apply the reflection rule to point [tex]\( P \)[/tex]:
- The x-coordinate of [tex]\( P \)[/tex] is [tex]\(-3\)[/tex]; it stays the same.
- The y-coordinate of [tex]\( P \)[/tex] is [tex]\( 4 \)[/tex]; its sign changes to [tex]\(-4\)[/tex].
4. Write the coordinates of the reflected point:
- The new coordinates after reflection are [tex]\( (-3, -4) \)[/tex].
Therefore, the reflection of point [tex]\( P \)[/tex] across the x-axis, denoted as [tex]\( R_{x-axis}(P) \)[/tex], is:
[tex]\[ R_{x-axis}(P) = (-3, -4) \][/tex]
[tex]\[
([-3],[-4])
\][/tex]
