Chapter 14.7, Problem 6CE

To determine

To describe : the transformations of $T^3$ .

Answer to Problem 6CE

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

  $15$ units to the right.

Explanation of Solution

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

  $\begin{array}{l}{T}^2\left(x,y\right)=T\left(T\left(x,y\right)\right)\\ \Rightarrow T\left(x+5,y\right)=\left(x+5+5,y\right)\\ \Rightarrow \left(x+10,y\right)\\ T^3\left(x,y\right)=T\left(T^2\left(x,y\right)\right)\\ \Rightarrow T\left(x+10,y\right)=\left(x+10+5,y\right)\\ \Rightarrow \left(x+15,y\right)\end{array}$

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

  $15$ units to the right.