For the cards in the card sort, I found the figures on a grid at betterlesson.com Before I copied them for students, I did add a few labeled points so they could be A and A'. I left some of them unlabeled on purpose so students could discuss that it could be a reflection or a translation depending on how vertices were labeled. (That part will hopefully take place further in the unit!) The cards that are not on a grid I made using Word. I added a few dilation images too that are on a grid in my added cards. The last page of the Word doc also has the transformation rule for each card. That file is linked here. Once you print both documents linked here, you'll have a set of transformations (translation, reflections, rotations & dilations that are both on and off a coordinate grid.
Here are a couple images of the "sort into two piles".