Chapter 12.5, Problem 19E

To determine

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

Explanation of Solution

Given information:

Consider the polygon with coordinates $\text{E}\left(1,0\right)$ , $\text{F}\left(1,4\right)$ and $\text{G}\left(4,3\right)$ .

The image after reflection in the x-axis is to translated using $\left(\text{x,y}\right)\to \left(\text{x}+5,\text{y}-1\right)$ .

Graph:

The reflection of the polygon is shown below:

The coordinates of reflected polygon is $\text{E'}\left(-1,0\right)$ , $\text{F'}\left(-1,4\right)$ and $\text{G'}\left(-4,3\right)$ .

The image after reflection in the x-axis is to translated using $\left(\text{x,y}\right)\to \left(\text{x}+5,\text{y}-1\right)$ .

The coordinates are $\text{A}\left(4,-1\right)$ , $\text{B}\left(4,3\right)$ and $\text{C}\left(1,2\right)$ .

The image is given below:

Interpretation:

The image formed is a triangle.