Chapter 14.8, Problem 10ST2

a.

To determine

To find the inverse transformation of the following.

Answer to Problem 10ST2

The inverse transformation of $D_{0,5}$ is $D_{0,\frac{1}{5}}$ .

Explanation of Solution

Given information: $D_{0,5}$

In general, the inverse of a transformation T is defined as the transformation S such that $S\circ T=I$ .

Therefore, the inverse transformation of $D_{0,5}$ is $D_{0,\frac{1}{5}}$

b.

To determine

To find the transformation of the following.

Answer to Problem 10ST2

The inverse transformation of $R_{0,-70}$ is $R_{0,70}$ .

Explanation of Solution

Given information:

  $R_{0,-70}$

In general, the inverse of a transformation T is defined as the transformation S such that $S\circ T=I$

Therefore, the inverse transformation of $R_{0,-70}$ is $R_{0,70}$ .

c.

To determine

To find the transformation of the following.

Answer to Problem 10ST2

The inverse transformation of $R_k$ is $R_k$ .

Explanation of Solution

Given information:

  $R_k$

In general, the inverse of a transformation T is defined as the transformation S such that $S\circ T=I$

Since $R_k\circ R_k=I$ , the inverse of $R_k$ is $R_k$ itself.

In symbols $R^{-1}{}_k=R_k.$

Therefore, the inverse transformation of $R_k$ is $R_k$ .

d.

To determine

To find the transformation of the following.

Answer to Problem 10ST2

The inverse transformation of $S:\left(x,y\right)\to \left(x+2,y-3\right)$ is $S^{-1}:\left(x,y\right)\to \left(x-2,y+3\right)$ .

Explanation of Solution

Given information:

  $S:\left(x,y\right)\to \left(x+2,y-3\right)$

In general, the inverse of a transformation T is defined as the transformation S such that $S\circ T=I$

Therefore, the inverse transformation of $S:\left(x,y\right)\to \left(x+2,y-3\right)$ is $S^{-1}:\left(x,y\right)\to \left(x-2,y+3\right)$ .