Chapter 9.4, Problem 14PPS

To determine

To graph:

Figure for given vertices and its image after composition of transformation.

Explanation of Solution

Given information:

  $\overline{AB}:A\left(-3,2\right),B\left(3,8\right)$

Translation: along $\langle 4,4\rangle$ .

Rotation: $90°$ about origin.

Graph:

  

Interpretation:

Rotation: $90°$ about origin.

  $\begin{array}{l}\left(x,y\right)\Rightarrow \left(-y,x\right)\\ A\left(-3,2\right)\Rightarrow A^{\text{'}}\left(-2,-3\right)\\ B\left(3,8\right)\Rightarrow B^{\text{'}}\left(-8,3\right)\end{array}$

Translation: along $\langle 4,4\rangle$ .

  $\begin{array}{l}\left(x,y\right)\Rightarrow \left(x+4,y+4\right)\\ A^{\text{'}}\left(-2,-3\right)\Rightarrow A^{\text{'}\text{'}}\left(2,1\right)\\ B^{\text{'}}\left(-8,3\right)\Rightarrow B^{\text{'}}{}^{\text{'}}\left(-4,7\right)\end{array}$