Question

pentagon jklmn is the image of pentagon jklmn under a reflection across the line y = -x followed by a translation.
write the rules for the reflection and translation.
reflection: (x, y) → ( , )
translation: (x, y) → ( , )

Explanation:

Step1: Find the reflection rule

The rule for reflection across the line \(y = -x\) is \((x,y)\to(-y,-x)\).

Step2: Find the translation rule

Let's take a point, say \(J(1,2)\). After reflection across \(y=-x\), it becomes \((-2,-1)\). The image \(J'(4,-2)\).
To get from \((-2,-1)\) to \((4,-2)\):
For the \(x -\)coordinate: \(4-(-2)=6\)
For the \(y -\)coordinate: \(-2-(-1)=-1\)
So the translation rule is \((x,y)\to(x + 6,y-1)\)

Answer:

Reflection: \((x,y)\to(-y,-x)\)
Translation: \((x,y)\to(x + 6,y-1)\)