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)

Question

asked Jul 22, 2018 164k views

2 Answers

Thomasmost · Answer 1 · 2018-07-28T10:56:37+0000

Answer:

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.