To determine which reflection of the point with coordinates (0, k) will produce an image at the same coordinates, we need to understand how reflections work.
1. Reflection across the x-axis:
- When reflecting a point across the x-axis, only the y-coordinate of the point changes its sign.
- The coordinates (x, y) transform to (x, -y).
- Applying this to our point (0, k), after reflection across the x-axis, the new coordinates will be (0, -k).
2. Reflection across the y-axis:
- When reflecting a point across the y-axis, only the x-coordinate of the point changes its sign.
- The coordinates (x, y) transform to (-x, y).
- Applying this to our point (0, k), after reflection across the y-axis, the new coordinates will be (0, k).
Now, we need to find which reflection produces the image at the same coordinates (0, k):
- Reflection across the x-axis changes the point (0, k) to (0, -k).
- Reflection across the y-axis keeps the point at (0, k).
Thus, reflecting the point across the y-axis will produce an image at the same coordinates (0, k).
Therefore, the correct answer is that a reflection of the point across the y-axis will produce an image at the same coordinates, (0, k).
The correct reflection that keeps the coordinates unchanged is indeed the reflection across the y-axis, making the final answer:
2
