1. Match the quote to the correct coordinate notation. One is done for you.
Rules for Reflection on a Coordinate
Plane
Quote
D. Reflection across the $x$-axis
\[
(x, y) \rightarrow(x,-y)
\]
Reflection across the y-axis
\[
(x, y) \rightarrow(-x, y)
\]
Reflection across line $y=x$
\[
(x, y) \rightarrow(y, x)
\]
Reflection across line $y=-x$
\[
(x, y) \rightarrow(-y,-x)
\]
B. "To reflect the figure, all $x$ values will be the opposite sign of the $y$ values; all $y$ values will be the opposite sign of the $x$ values."

C. "To reflect the figure, all $x$ values will be the $y$ values; all $y$ values will be the $x$ values."
D. "To reflect the figure, all $x$ values will remain the same; all $y$ values will take the opposite sign."

Step 1 ：Match the given quotes to the correct reflection rules on a coordinate plane.

Step 2 ：The quote 'To reflect the figure, all x values will be the opposite sign of the y values; all y values will be the opposite sign of the x values.' matches with the rule for reflection across line \(y=-x\), which is \((x, y) \rightarrow(-y,-x)\).

Step 3 ：The quote 'To reflect the figure, all x values will be the y values; all y values will be the x values.' matches with the rule for reflection across line \(y=x\), which is \((x, y) \rightarrow(y, x)\).

Step 4 ：The quote 'To reflect the figure, all x values will remain the same; all y values will take the opposite sign.' matches with the rule for reflection across the \(x\)-axis, which is \((x, y) \rightarrow(x,-y)\).

Step 5 ：The rule for reflection across the \(y\)-axis, which is \((x, y) \rightarrow(-x, y)\), is not mentioned in the quotes.

Step 6 ：\(\boxed{\text{Final Answer:}}\)

Step 7 ：Quote B matches with the rule for reflection across line \(y=-x\), which is \((x, y) \rightarrow(-y,-x)\).

Step 8 ：Quote C matches with the rule for reflection across line \(y=x\), which is \((x, y) \rightarrow(y, x)\).

Step 9 ：Quote D matches with the rule for reflection across the \(x\)-axis, which is \((x, y) \rightarrow(x,-y)\).

Step 10 ：The rule for reflection across the \(y\)-axis, which is \((x, y) \rightarrow(-x, y)\), is not mentioned in the quotes.