Answer:
(-2,4)
Step-by-step explanation:
[tex]\text{pre-image}->\text{image}[/tex]
[tex](x,y)->(x+3,y-3)[/tex]
[tex](x,y)->(1,1)[/tex]
This implies [tex](x+3,y-3)=(1,1)[/tex].
This means [tex]x+3=1[/tex] and [tex]y-3=1[/tex].
Subtract 3 on both sides for first equation: [tex]x=1-3=-2[/tex].
Add 3 on both sides for the second equation: [tex]y=1+3=4[/tex].
So the pre-image (x,y) is (-2,4) if the image is (1,1).
Let's check:
[tex](x,y)->(x+3,y-3)[/tex]
[tex](-2,4)->(-2+3,4-3)[/tex]
[tex](-2,4)->(1,1)[/tex]
So the solution has been checked and verified.
