Question

what is a rule for the translation that maps △rst to △rst? a t(-7,3)

Explanation:

Step1: Find x - coordinate change

Let's take a point, say $R(2,2)$. Its image is $R'(- 5,5)$. The change in the x - coordinate is $-5 - 2=-7$.

Step2: Find y - coordinate change

The change in the y - coordinate of point $R$ is $5 - 2 = 3$.
For any point $(x,y)$ in $\triangle{RST}$, the translation rule is $(x,y)\to(x - 7,y + 3)$.

Answer:

The translation rule is $(x,y)\to(x - 7,y + 3)$