Chapter 14.2A, Problem 19A

Point $P^{\prime }$ is the image of P (not shown) under a glide reflection determined by the slide arrow $\stackrel{\to }{AB}$ and line $\mathcal{l}$ parallel to $\stackrel{\leftrightarrow }{AB}$ .

a. Describe the transformation that takes $P^{\prime }$ back to P.

b. Construct any $\Delta DEF$ and find its image $\Delta D^{\prime }{E}^{\prime }{F}^{\prime }$ under the glide reflection described earlier in the question. Then apply the same glide reflection to $\Delta D^{\prime }{E}^{\prime }{F}^{\prime }$ to find its image $\Delta D^{″}{E}^{″}{F}^{″}$. What seems to be a single transformation under which the image of $\Delta DEF$ will be $\Delta D^{″}{E}^{″}{F}^{″}$?