Chapter 12.5, Problem 18E

To determine

To draw a polygon, reflection of the polygon and the final image.

Explanation of Solution

Given information:

Consider the polygon with coordinates $\text{A}\left(-5,3\right)$ , $\text{B}\left(-2,3\right)$ , $\text{C}\left(-1,1\right)$ and $\text{D}\left(-4,1\right)$ .

The image after reflection in the x-axis is to translated using $\left(\text{x,y}\right)\to \left(\text{x}+2,\text{y}+4\right)$ .

Graph:

The reflection of the polygon is shown below:

The image after reflection in the x-axis is to translated using $\left(\text{x,y}\right)\to \left(\text{x}+2,\text{y}+4\right)$ .

The coordinates are $\text{A}\left(-3,1\right)$ , $\text{B}\left(0,1\right)$ , $\text{C}\left(1,3\right)$ and $\text{D}\left(-2,3\right)$ .

The image is given below:

Interpretation:

The image formed is a parallelogram.