Question

A point has the coordinates (0, k).

Which reflection of the point will produce an image at the same coordinates, (0, k)?

a reflection of the point across the x-axis
a reflection of the point across the y-axis
a reflection of the point across the line y = x
a reflection of the point across the line y = –x

Answer 1

To determine which reflection of the point (0, k) will produce an image at the same coordinates (0, k), let’s analyze each reflection option:

1. **Reflection across the x-axis**:
- The x-axis reflection of the point (0, k) will be (0, -k).
- Not the same as (0, k) unless k = 0.

2. **Reflection across the y-axis**:
- The y-axis reflection of the point (0, k) will be (0, k).
- This results in the same coordinates (0, k).

3. **Reflection across the line y = x**:
- The reflection of the point (0, k) across the line y = x will be (k, 0).
- Not the same as (0, k).

4. **Reflection across the line y = –x**:
- The reflection across the line y = –x will yield (-k, 0).
- Not the same as (0, k).

Based on this analysis, the only reflection that will produce the same coordinates (0, k) is **the reflection across the y-axis**.