Answer:
The preimage is [tex](6,0)[/tex]
Step-by-step explanation:
The given point is (4,3).
The translation rule is
[tex]T:(x,y)\rightarrow (x-2,y+3)[/tex]
Let [tex](a,b)[/tex] be the preimage.
Then,
We apply this rule to the preimage to obtain;
[tex]T:(a,b)\rightarrow (a-2,b+3)[/tex]
This implies that;
[tex]a-2=4[/tex]
[tex]\Rightarrow a=4+2[/tex]
[tex]\Rightarrow a=6[/tex]
Also,
[tex]b+3=3[/tex]
[tex]\Rightarrow b=3-3[/tex]
[tex]\Rightarrow b=0[/tex]
Hence the preimage is [tex](6,0)[/tex]
