Question

2 of 32 of 3 Items Question Select the rule for this reflection. (1 point) Responses Reflection across y-axis Reflection across y-axis y=x y=x Reflection across x-axis Reflection across x-axis y=-x y=-x Skip to navigation page 5 of 5

Answer 1

To determine the rule for a reflection, we need to consider the line across which the reflection occurs.

1. **Reflection across the y-axis**: When reflecting a point (x, y) across the y-axis, the x-coordinate changes sign, resulting in the point (-x, y).

2. **Reflection across the x-axis**: When reflecting a point (x, y) across the x-axis, the y-coordinate changes sign, resulting in the point (x, -y).

3. **Reflection across the line y=x**: When reflecting a point (x, y) across the line y=x, the coordinates swap places, resulting in the point (y, x).

4. **Reflection across the line y=-x**: When reflecting a point (x, y) across the line y=-x, the coordinates swap and change sign, resulting in the point (-y, -x).

Based on these definitions:
- The response option "Reflection across y-axis" is a valid description of one type of reflection.
- "Reflection across x-axis" is another valid reflection.
- "y=x" and "y=-x" describe specific lines but do not refer directly to the reflection itself without additional context.

If the question is asking for the specific reflection rule involving points, and without additional details, the appropriate option would depend on the context or the line specified. However, since both "Reflection across y-axis" and "Reflection across x-axis" are valid reflection rules, the line or the context should clarify the situation.

Please choose the option that seems most appropriate based on the context of your problem. If provided with specific coordinates or a graph, we could provide a clearer answer.