Chapter 14.7, Problem 23CE

a.

To determine

To state : the inverse of the transformation.

Answer to Problem 23CE

The inverse of $R_1$ is $R_1$ .

Explanation of Solution

Given information : The transformation is $R_1$ .

Calculation :

  $\begin{array}{l}{R}_1\cdot R_1=I\\ R_1{}^{-1}=R_1\end{array}$

Hence, $R_1$ is the inverse of itself.

To determine

To state : the inverse of the transformation.

Answer to Problem 23CE

The inverse of $R_{0\cdot 30}$ is $R_{0\cdot -30}$ .

Explanation of Solution

Given information : The transformation is $R_{0\cdot 30}$ .

Calculation :

  $R_{0\cdot 30}=R_{0\cdot -30}$

So, $R_{0\cdot -30}$ bring the change back.

c.

To determine

To state : the inverse of the transformation.

Answer to Problem 23CE

The inverse of $T\left(x,y\right)\to \left(x-4,y+1\right)$ is $\left(x,y\right)$

Explanation of Solution

Given information : The transformation is $T\left(x,y\right)\to \left(x-4,y+1\right)$ .

Calculation :

  $\begin{array}{l}T\left(x,y\right)\to \left(x-4,y+1\right)\\ T^{-1}\left(T\left(x,y\right)\right)\\ \Rightarrow T^{-1}\left(x-4,y+1\right)\\ \Rightarrow x-4+4,y+1-1\\ \Rightarrow \left(x,y\right)\end{array}$

d.

To determine

To state : the inverse of the transformation.

Answer to Problem 23CE

The inverse of $D_{0\cdot -1}$ is $D_{0\cdot 1}$ .

Explanation of Solution

Given information : The transformation is $D_{0\cdot -1}$ .

Calculation :

  $D_{0\cdot -1}=D_{0\cdot 1}$

The point in opposite side and length of segment is same