We have E(7,-2) and E'(2,0).
We can think of E' as the image of E after a translation (a,b), where we have to find the values of a and b.
We can write:
[tex]E(7,-2)\longrightarrow E^{\prime}(7+a,-2+b)=E^{\prime}(2,0)[/tex]
Then, we can find a and b as:
[tex]\begin{gathered} 7+a=2\longrightarrow a=2-7=-5 \\ -2+b=0\longrightarrow b=0+2=2 \end{gathered}[/tex]
The translation is then (-5,2).
Then, we can write the rule as:
[tex](x,y)\longrightarrow(x-5,y+2)[/tex]
Answer: (x,y) --> (x-5,y+2)
