The translation vector <2, 7> means that from an initial position, the vector moves two units to the right (because 2 is positive) and 7 units up (because 7 is positive as well).
Meaning, for any x in the coordinate plane, we will be adding 2. So, that is x + 2.
On the other hand, for any y in the coordinate plane, we will be adding 7. So, that is y + 7.
To complete the translation function:
[tex](x,y)\rightarrow(x+2,y+7)_{}[/tex]
