Question

pentagon ( abcde ) is the image of pentagon ( abcde ) under a translation right 7 units and up 7 units followed by a reflection.

write the rules for the translation and reflection.

translation: ( (x,y)\to(quad,quad) )

reflection: ( (x,y)\to(quad,quad) )

Explanation:

Step1: Determine the translation rule

A translation right \(7\) units and up \(7\) units. For a point \((x,y)\), the \(x\) - coordinate increases by \(7\) (right translation) and the \(y\) - coordinate increases by \(7\) (up translation). So the translation rule is \((x,y)\to(x + 7,y+7)\).

Step2: Determine the reflection rule

Looking at the graph, after the translation, the reflection is over the \(x\) - axis. For a point \((x,y)\), the reflection over the \(x\) - axis changes the sign of the \(y\) - coordinate. So the reflection rule is \((x,y)\to(x,-y)\).

Answer:

Translation: \((x,y)\to(x + 7,y + 7)\)
Reflection: \((x,y)\to(x,-y)\)