Answer :
To determine the coordinates of point [tex]\( P' \)[/tex], which is the reflection of point [tex]\( P \)[/tex] over the x-axis, we need to follow a specific rule for reflections over the x-axis:
Reflection over the x-axis:
- When a point [tex]\((x, y)\)[/tex] is reflected over the x-axis, the x-coordinate remains the same, but the y-coordinate is negated (changes its sign).
Given the coordinates of point [tex]\( P \)[/tex] are [tex]\((4, 3)\)[/tex]:
1. Identifying the x and y coordinates of [tex]\( P \)[/tex]:
- The x-coordinate of [tex]\( P \)[/tex] is 4.
- The y-coordinate of [tex]\( P \)[/tex] is 3.
2. Reflecting [tex]\( P \)[/tex] over the x-axis:
- The x-coordinate remains unchanged: [tex]\( x' = 4 \)[/tex].
- The y-coordinate is negated: [tex]\( y' = -3 \)[/tex].
Thus, the coordinates of point [tex]\( P' \)[/tex] are [tex]\((4, -3)\)[/tex].
Conclusion:
Point [tex]\( P' \)[/tex], which is the reflection of point [tex]\( P \)[/tex] [tex]\((4, 3)\)[/tex] over the x-axis, has the coordinates [tex]\((4, -3)\)[/tex].
Reflection over the x-axis:
- When a point [tex]\((x, y)\)[/tex] is reflected over the x-axis, the x-coordinate remains the same, but the y-coordinate is negated (changes its sign).
Given the coordinates of point [tex]\( P \)[/tex] are [tex]\((4, 3)\)[/tex]:
1. Identifying the x and y coordinates of [tex]\( P \)[/tex]:
- The x-coordinate of [tex]\( P \)[/tex] is 4.
- The y-coordinate of [tex]\( P \)[/tex] is 3.
2. Reflecting [tex]\( P \)[/tex] over the x-axis:
- The x-coordinate remains unchanged: [tex]\( x' = 4 \)[/tex].
- The y-coordinate is negated: [tex]\( y' = -3 \)[/tex].
Thus, the coordinates of point [tex]\( P' \)[/tex] are [tex]\((4, -3)\)[/tex].
Conclusion:
Point [tex]\( P' \)[/tex], which is the reflection of point [tex]\( P \)[/tex] [tex]\((4, 3)\)[/tex] over the x-axis, has the coordinates [tex]\((4, -3)\)[/tex].
