Question

pentagon defgh is the image of pentagon defgh under a reflection across the y-axis followed by a translation.
write the rules for the reflection and translation.
reflection: (x, y) ↦ (\boxed{ }, \boxed{ })
translation: (x, y) ↦ (\boxed{ }, \boxed{ })

Explanation:

Step1: Find the reflection rule

The rule for reflection across the \(y -\)axis is \((x,y)\to(-x,y)\). For example, if we take a general point \((x,y)\) and reflect it across the \(y -\)axis, the \(x -\)coordinate changes its sign and the \(y -\)coordinate remains the same.

Step2: Find the translation rule

Let's use a point to find the translation. Take point \(D(-8,-2)\). After reflection across the \(y -\)axis, it becomes \((8,-2)\). The image of \(D\) is \(D'(8,2)\).
To get from \((8,-2)\) to \((8,2)\), we add \(4\) to the \(y -\)coordinate. The translation rule is \((x,y)\to(x,y + 4)\)

Answer:

Reflection: \((x,y)\to(-x,y)\)
Translation: \((x,y)\to(x,y + 4)\)