Answer:
The correct option is A.
Step-by-step explanation:
The transformation T is given as
[tex]T:(x,y)\rightarrow (x+4,y+3)[/tex]
Let the transformation T⁻¹ is defined as
[tex]T^{-1}:(x,y)\rightarrow (x+a,y+b)[/tex]
If T and T⁻¹ are inverses of each other, then
[tex]T(T^{-1}(x))=x[/tex]
[tex]T(x+a)=x[/tex]
[tex]x+a+4=x[/tex]
[tex]a=-4[/tex]
The value of a is -4.
If T and T⁻¹ are inverses of each other, then
[tex]T(T^{-1}(y))=y[/tex]
[tex]T(y+b)=y[/tex]
[tex]y+b+3=y[/tex]
[tex]b=-3[/tex]
The value of b is -3.
The transformation T⁻¹ is defined as
[tex]T^{-1}:(x,y)\rightarrow (x-4,y-3)[/tex]
Therefore the correct option is A.
