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 $y = -x$ has the rule $(x,y)\to(-y,-x)$. Reflection over the line $y=x$ has the rule $(x,y)\to(y,x)$.

Step2: Analyze the transformation

By observing the coordinates of the pre - image and image points of the triangle, we can see that the rule for the reflection is $(x,y)\to(-y,-x)$ which is reflection over the line $y=-x$.

Answer:

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