Question

Its geometry how do write a rule to describe the transformation

Answer 1

In geometry, "translation" simply means MOVING ...... without rotating, resizing or anything else, just moving. Here's an example to help you better understand.
Example: when we want to say a shape gets moved 30 Units in the "X" direction, and 40 Units in the "Y" direction, we can write:
\[(x,y)-->(x+30,y+40)\]
Which says "all the x and y coordinates will become x+30 and y+40"

Answer 2

I think this is how I understood your question, but if I am not answering your answer correcting, please do let me know.