We have:
A ( -3, 6 ) ; A' ( 3, -6 )
and
A (x,y) --> A' ( x + a, y + b )
So, A ( -3, 6 ) --> A' ( -3 + a, 6 + b ) or A ( -3, 6 ) --> A' ( 3, -6 )
Therefore:
[tex]\begin{gathered} -3+a=3 \\ -3+a+3=3+3 \\ a=6 \end{gathered}[/tex]
and
[tex]\begin{gathered} 6+b=-6 \\ 6+b-6=-6-6 \\ b=-12 \end{gathered}[/tex]
Answer: The rule is:
[tex](x,y)\rightarrow(x+6,y-12)[/tex]
