Chapter 14.7, Problem 9CE

To determine

To describe : the transformations of $T\cdot T^{-1}$ .

Answer to Problem 9CE

The translation shifts point $\left(x,y\right)$ on same point.

Explanation of Solution

Given information : The translation $T$ maps all points five units to the right. The figure shown below:

  $\begin{array}{l}T\cdot T^{-1}\\ \Rightarrow T\left(T^{-1}\left(x,y\right)\right)\\ \Rightarrow T\left(x-5,y\right)\\ \Rightarrow x^{-5+5},y\\ \Rightarrow \left(x,y\right)\end{array}$

Thus, the translation shifts point $\left(x,y\right)$ on same point.