Chapter 4.2, Problem 67SR

a.

To determine

To describe: the reflection and transformation combination shown in the figure.

Answer to Problem 67SR

6 units to the right.

Explanation of Solution

Given:

The combination of reflection and transformation is called glide reflection. An example is a set of foot-print:

  

Calculation:

The set of footprints is as follows.

  

The objective is to describe the reflection and transformation combination of the graph.

From the graph it is seen that the object is reflected over the x-axis and then translated 6 units to the right.

b.

To determine

To write: the two-matrix operation that can be used to find the coordinates points of C.

Answer to Problem 67SR

  $\left[\begin{array}{l}10\\ 0-1\end{array}\right]\text{ and }\left[\begin{array}{l}6\\ 0\end{array}\right]$ .

Explanation of Solution

Given:

The combination of reflection and transformation is called glide reflection. An example is a set of foot-print:

  

Calculation:

The objective is to write two matrix operation that can be used to find the coordinates of point C.

The coordinates of point C can be found out by multiply the coordinates by $\left[\begin{array}{l}10\\ 0-1\end{array}\right]$ and then add the result to $\left[\begin{array}{l}6\\ 0\end{array}\right]$ .

Therefore, the matrices are $\left[\begin{array}{l}10\\ 0-1\end{array}\right]\text{ and }\left[\begin{array}{l}6\\ 0\end{array}\right]$ .

c.

To determine

To check: whether it matters that which operation is first.

Answer to Problem 67SR

No.

Explanation of Solution

Given:

The combination of reflection and transformation is called glide reflection. An example is a set of foot-print:

  

Calculation:

No, since the translation does not change the y - coordinate, it does not matter whether or not you do the translation or reflection first. However, if the translation did change the y-coordinate, the order would be important.

d.

To determine

To write: the coordinates of the next two foot-prints.

Answer to Problem 67SR

  $\left[\begin{array}{l}10\\ 0-1\end{array}\right]\text{ and }\left[\begin{array}{l}6\\ 0\end{array}\right]$ .

Explanation of Solution

Given:

The combination of reflection and transformation is called glide reflection. An example is a set of foot-print:

  

Calculation:

The objective is to find the coordinates of the next two-foot print.

The next two-foot print is calculated below:

  $\begin{array}{l}B\left(11,2\right)\to C\left(11+6,-2\right)\\ \to C\left(17,-2\right)\\ C\left(17,-2\right)\to D\left(17+6,-\left(-2\right)\right)\\ \to D\left(23,2\right)\end{array}$

Therefore, the expression is $C\left(17,-2\right),D\left(23,2\right)$