According to the graph, we have:
- The coordinates of the RSTU square are:
R(-6, 4)
S(-2,4)
T(-2, 8)
U(-6, 8)
- The coordinates of the R'S'T'U' square are:
R'(3, -1)
S'(7, -1)
T'(7, 3)
U'(3, 3)
Therefore, applying the translation rule (x,y) --> (x + a, y + b), so:
- For R
[tex](-6+a,4+b)\rightarrow(3,-1)[/tex]With this we have the following equations:
[tex]\begin{gathered} -6+a=3 \\ -6+a+6=3+6 \\ a=9 \\ and \\ 4+b=-1 \\ 4+b-4=-1-4 \\ b=-5 \end{gathered}[/tex]So, a = 9 and b = -5
Next, the translation rule is given by:
(x, y) ---> (x + 9, y - 5)
Answer: (x, y) ---> (x + 9, y - 5)