To determine the coordinates of the image of point [tex]\( P(3, -4) \)[/tex] under a reflection in the x-axis, let's follow these steps:
1. Understand Reflection in the X-Axis:
- Reflecting a point over the x-axis means flipping its y-coordinate while keeping its x-coordinate the same. Essentially, if you have a point [tex]\( (x, y) \)[/tex], its reflection over the x-axis will be [tex]\( (x, -y) \)[/tex].
2. Apply Reflection Rules to Point [tex]\( P(3, -4) \)[/tex]:
- Given the point [tex]\( P(3, -4) \)[/tex], the x-coordinate remains the same, which is 3.
- For the y-coordinate, we need to change its sign. The y-coordinate of [tex]\( P \)[/tex] is -4, so the reflected y-coordinate will be [tex]\( -(-4) = 4 \)[/tex].
3. Determine the Coordinates of the Reflected Point:
- Therefore, the coordinates of the image of point [tex]\( P(3, -4) \)[/tex] under a reflection in the x-axis are [tex]\( (3, 4) \)[/tex].
4. Check Against the Given Options:
- A. [tex]\( (-3, -4) \)[/tex] is not correct because the x-coordinate has been incorrectly changed.
- B. [tex]\( (-4, 3) \)[/tex] is incorrect as it incorrectly changes both x and y coordinates.
- C. [tex]\( (3, 4) \)[/tex] matches our result perfectly.
- D. [tex]\( (4, -3) \)[/tex] incorrectly swaps and changes the signs of the coordinates.
Hence, the correct answer is:
[tex]\[ C. (3, 4) \][/tex]
