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.