Chapter 14.7, Problem 10CE

To determine

To describe : the transformations of ${\left(T^{-1}\right)}^{-1}$ .

Answer to Problem 10CE

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

  $10$ units to the left.

Explanation of Solution

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

  $\begin{array}{l}{\left(T^{-1}\right)}^{-1}\\ \Rightarrow T^{-1}=\left(x-5,y\right)\\ \Rightarrow {\left(T^{-1}\right)}^{-1}=\left(x-5-5,y\right)\\ \Rightarrow {\left(T^{-1}\right)}^{-1}=\left(x-10,y\right)\end{array}$

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

  $10$ units to the left.