Question

For the transformation T, what is T-1?

T : (x, y) (x + 4, y + 3)
T-1: (x, y)

A.) (x - 4, y - 3)
B.) (-4x, -3y)
C.) (x + 3, y + 2)

Answer 1

A.) (x-4 , y-3)
inverse of addition is subtraction.

Answer 2

The correct option is A.

Explanation:

The transformation T is given as

`T:(x,y)\rightarrow (x+4,y+3)`

Let the transformation T⁻¹ is defined as

`T^(-1):(x,y)\rightarrow (x+a,y+b)`

If T and T⁻¹ are inverses of each other, then

`T(T^(-1)(x))=x`

`T(x+a)=x`

`x+a+4=x`

`a=-4`

The value of a is -4.

If T and T⁻¹ are inverses of each other, then

`T(T^(-1)(y))=y`

`T(y+b)=y`

`y+b+3=y`

`b=-3`

The value of b is -3.

The transformation T⁻¹ is defined as

`T^(-1):(x,y)\rightarrow (x-4,y-3)`

Therefore the correct option is A.