Answer:
The rule of translation : 
The vertices of image is R'(2,-9), S'(1,-9), T'(6,-3) and U'(2,-3).
Step-by-step explanation:
The vertices of a rectangle are R(-5,-5), S(-6,-5), T(-1,1), U(-5,1).
It is given that a translation maps R to the point (2,-9).
Difference between x-coordinates:

Difference between y-coordinates:

The x-coordinate increased by 7 and y-coordinate decreased by 4. It means the figure shifts 7 units right and 4 units down.
The rule of translation is

The vertices of image are




Therefore, the vertices of image are R'(2,-9), S'(1,-9), T'(6,-3) and U'(2,-3).