Question

1. write a glide reflection that maps the preimage to the image on the following graph.

Explanation:

Step1: Determine the reflection line

A glide reflection is a composition of a reflection and a translation. First, observe the orientation of the pre - image and image. The pre - image and image are mirror images with respect to the \(x\) - axis. The rule for reflection over the \(x\) - axis is \((x,y)\to(x, - y)\).

Step2: Determine the translation

After reflection over the \(x\) - axis, we need to translate the figure. Let's take a point from the pre - image. For example, a point \((-4,1)\) in the pre - image. After reflection over the \(x\) - axis, it becomes \((-4,-1)\). The corresponding point in the image is \((1,-1)\). The translation rule from \((-4,-1)\) to \((1,-1)\) is \((x,y)\to(x + 5,y)\) (using the formula \(x_{2}-x_{1}\) for the \(x\) - translation, \(1-(-4)=5\) and \(y_{2}-y_{1}=-1-(-1) = 0\) for the \(y\) - translation).

Answer:

Reflect over the \(x\) - axis and then translate \(5\) units to the right. The glide - reflection rule is \((x,y)\to(x + 5,-y)\)