Sure, let's find the reflection of the point [tex]\( P = (3, 4) \)[/tex] across the x-axis.
### Step-by-Step Solution:
1. Identify the coordinates of the point [tex]\( P \)[/tex]:
[tex]\( P = (3, 4) \)[/tex]
Here, the x-coordinate is 3 and the y-coordinate is 4.
2. Understand the reflection process across the x-axis:
- When reflecting a point across the x-axis, the x-coordinate remains unchanged.
- The y-coordinate changes to its opposite (negative) value.
3. Apply the reflection process:
- The x-coordinate of [tex]\( P \)[/tex] remains the same: [tex]\( 3 \)[/tex].
- The y-coordinate of [tex]\( P \)[/tex] becomes the opposite: [tex]\( -4 \)[/tex].
Therefore, the reflected point [tex]\( R_{x-axis}(P) \)[/tex] is:
[tex]\[ (3, -4) \][/tex]
So, [tex]\( R_{x-axis}(P) = (3, -4) \)[/tex].
The solution:
[tex]\[ ([3], [-4]) \][/tex]
This gives us the final reflected point across the x-axis.
