Question

what is the rule for the reflection?
( r_{y = x}(x,y)\to(-y,-x) )
( r_{y=-x}(x,y)\to(-y,-x) )
( r_{y = x}(x,y)\to(y,x) )
( r_{y=-x}(x,y)\to(y,x) )

Explanation:

Step1: Recall reflection rules

• Reflection over the line \( y = x \): \( (x,y)\to(y,x) \)
• Reflection over the line \( y=-x \): \( (x,y)\to(-y,-x) \)

Step2: Analyze the transformation

Let's assume a general point \((x,y)\) in the original figure. After reflection, if we consider the mapping of coordinates. For example, if we take a point \((a,b)\) in the pre - image and its image \((-b,-a)\) in the post - image. This mapping \( (x,y)\to(-y,-x) \) is the rule for reflection over the line \( y =-x\). So the rule for the reflection is \( r_{y=-x}(x,y)\to(-y,-x) \)

Answer:

B. \( r_{y = -x}(x,y)\to(-y,-x) \)