To determine the correct reflection rule, we need to know the orientation of the reflection line.
- Reflection across the y-axis swaps the sign of the x-coordinates. The rule would look like \( (x, y) \rightarrow (-x, y) \).
- Reflection across the x-axis swaps the sign of the y-coordinates. The rule would look like \( (x, y) \rightarrow (x, -y) \).
- Reflection across the line \( y = x \) swaps the x and y coordinates. The rule would look like \( (x, y) \rightarrow (y, x) \).
- Reflection across the line \( y = -x \) also swaps the coordinates but negates them. The rule would be \( (x, y) \rightarrow (-y, -x) \).
Based on the options provided, the reflection rules match the following:
- Reflection across the y-axis: \( (x, y) \rightarrow (-x, y) \)
- Reflection across the x-axis: \( (x, y) \rightarrow (x, -y) \)
- Reflection across the line \( y = x \): \( (x, y) \rightarrow (y, x) \)
- Reflection across the line \( y = -x \): \( (x, y) \rightarrow (-y, -x) \)
So, if you are looking for the direct match from the options given:
- Reflection across y-axis
- Reflection across y-axis
- y = -x
- y = -x
- Reflection across x-axis
- Reflection across x-axis
- y = x
Given these responses, the full set is specified without clear associations, but you can select from the first two directly if you refer to the mentioned rules for visualization.
Please choose the one that applies to your context or requirement!
1 answer