A point has the coordinates (0, k).

Question

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.