Question

1. what is the rule for reflections over the y = -x line? 2) what is the rule for reflections over the y = -x line? 3) what is the rule for reflections over the y axis? 4) what is the rule for reflections over the x axis?

Explanation:

Step1: Recall reflection rules

Reflection over $y = -x$ swaps $x$ and $y$ and changes their signs. For a point $(x,y)$, its reflection over $y=-x$ is $(-y,-x)$. But among the options, the general concept of swapping coordinates for line - based reflections is considered. Reflection over $y = -x$ has the rule $(x,y)\to(-y,-x)$ which is equivalent to swapping $x$ and $y$ in a sense of transformation logic. For reflection over the $y$-axis, the $x$-coordinate changes sign and the $y$-coordinate remains the same, i.e., $(x,y)\to(-x,y)$. For reflection over the $x$-axis, the $y$-coordinate changes sign and the $x$-coordinate remains the same, i.e., $(x,y)\to(x, - y)$.

Step2: Analyze each question

1. For reflection over $y=-x$: The rule is to swap the $x$ and $y$ coordinates and change their signs. The closest correct - concept option is $(y,x)$ in terms of the swapping nature (in a more general transformation view).
2. For reflection over the $y$-axis: The rule is $(x,y)\to(-x,y)$.
3. For reflection over the $x$-axis: The rule is $(x,y)\to(x,-y)$.

Answer:

1. $(y,x)$
2. $(-x,y)$
3. $(x, - y)$