Chapter 9.4, Problem 4CYU

To determine

To describe: The single transformation that maps $S$ onto $S\text{'}\text{'}$ .

Answer to Problem 4CYU

The required figure is shown in figure (3).

Explanation of Solution

Given:

The given figure is as follows.

  

Figure (1)

Calculation:

Firstly, reflect the triangle $S$ in line $m$ as shown in the below figure.

  

Figure (2)

Now, reflect the triangle $S\text{'}$ in line $P$ as shown in the below figure.

  

Figure (3)

Since, the composition of two reflections in parallel lines can be described by a translation vector that is perpendicular to the two lines and twice the distance between the two lines.

Therefore, the composition of two reflections in parallel vertical lines $m$ and $p$ is equivalent to a horizontal translation right $2\times 1.5=3\text{inches}$ .