Chapter 11.6, Problem 15HP

To determine

To find: The transformations that map $\overline{XY}\text{ onto }\overline{X\text{'}Y\text{'}}$

Answer to Problem 15HP

Reflection about x = 3 and then shift 3 unit left.

Explanation of Solution

Given: Line segment $\overline{XY}$ has endpoints at $X\left(3,1\right)$ and $Y\left(-2,0\right)$ . After series of transformation, its image has endpoints at $X\text{'}\left(0,1\right)\text{ and }Y\text{'}\left(5,0\right)$ .

First plot the image.

  

First reflect the points about the line $x=3$ .

  $\begin{array}{l}X\left(3,1\right)\underrightarrow{\text{Reflection about }x-\text{axis}}{X}_{\text{'}}\left(3,1\right)\\ Y\left(-2,0\right)\underrightarrow{\text{Reflection about }x-\text{axis}}{Y}_{\text{'}}\left(8,0\right)\end{array}$

Shift 3-unit left.

  $\begin{array}{l}{X}_{\text{'}}\left(3,1\right)\underrightarrow{\text{shift 3 unit left}}X\text{'}\left(0,1\right)\\ Y_{\text{'}}\left(8,0\right)\underrightarrow{\text{shift 3 unit left }}Y\text{'}\left(5,0\right)\end{array}$