Identifying type of transformation

transformation see maps negative 2 3 2 4 negative 1 so let me do negative 2 comma 3 and it maps that to 4 negative 1 to 4 negative 1 and point negative 5 comma 5 negative 5 comma 5 negative 5 comma 5 it maps that to 7 negative 3 to 7 negative 3 so 7 negative 3 and so let's think about this a little bit how could we get from this point to this point and that point to that point now it's tempting to view this that may be a translation is possible because if you imagined a line if you imagined a line like that you can say hey let's just shift this whole thing down and then to the right these two things happen to have the same slope now they both have a slope of negative 2/3 and so this point would map to this point and that point would map to that point but that's not what we want we don't want negative 2/3 to map to 7 negative 3 we want negative 2/3 to map to 4 negative 1 so you could get this line over this line but we won't map the points that we want to map so this would this can't be at least I can't think of a way that this could actually be that this could actually be a translation now let's think about let's think about whether our transformation could be a reflection well if we imagine a line that has to see these both have a slope of negative 3 these both have a slope of negative 2/3 so if you imagine a slope that had a line that has a slope of positive 3 halves a positive 3 halves that was equidistant from both and I don't know if this is let's see is this equidistant is this equidistant from both of them it's either going to be that line or this line right over or that line actually that line looks better so that one and I once again I'm just eyeballing it so a line that has slope positive three-halves so this one looks right in between the two or actually it could be someplace in between but either way we just have to think about it qualitatively if you had a line that looked something like that and if you were to reflect over this line if you were to reflect over this line then this point would map to this point which is what we want and this purple point negative five comma five would map to that point it would be reflected over so it's pretty clear that this could be a reflection now rotation actually makes even more sense or at least in my brain makes a little more sense if you were to rotate around at this point right over here this point would map to that point and that map point would map to that point so a rotation also seems like a possibility for transformation see now let's think about transformation D let's think about transformation D we are going from 4 negative 1 4 negative 1 so that's 4 negative 1 2 7 negative 3 2 7 negative 3 actually maybe I'll put that magenta as well 2 7 negative 3 just like that and we want to go from negative 5 5 so negative 5 5 negative 5 5 to negative 2 to negative 2 3 negative 2 3 so I could definitely imagine a translation right over here this point went 3 to the right and 2 down this point went 3 to the right and 2 down so a translation definitely makes sense now let's think about a reflection so it would be tempting it would be tempting to let's see if I were to to get from this point to this point I could reflect around that but that won't help this one over here and for to get from that point to that point I could reflect around that but once again that's not going to help that point over there so a reflection really doesn't seem to do the trick and what about a rotation well to go from this point to this point we could rotate around this point we could go there but that won't help that won't help this point right over here while this is rotating there this point is going to rotate around like that it's going to end up someplace out here so that's not going to help so it looks like this is this one can only be a translation