Question

kite pqrs is the image of kite pqrs 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: Recall reflection rule

The rule for reflecting a point $(x,y)$ across the line $y = x$ is $(x,y)\to(y,x)$.

Step2: Analyze translation

Let's take a point, say $P(- 1,-2)$. After reflection across $y = x$, it becomes $P_1(-2,-1)$. And the final - image $P'(7,1)$. To get from $P_1(-2,-1)$ to $P'(7,1)$, we add $9$ to the $x$ - coordinate and $2$ to the $y$ - coordinate. The translation rule is $(x,y)\to(x + 9,y + 2)$.

Answer:

Reflection: $(x,y)\to(y,x)$
Translation: $(x,y)\to(x + 9,y + 2)$