Identifying type of transformation

Transformation C maps negative 2, 3 to 4, negative 1. So let me do negative 2 comma 3, and it maps that to 4, negative 1. And point negative 5 comma 5, it maps that to 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 maybe a translation is possible. Because if you imagined a line like that, you could say, hey, let's just shift this whole thing down and then to the right. These two things happen to have the same slope. 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 can't be, at least I can't think of a way, that this could actually be a translation. Now let's think about whether our transformation could be a reflection. Well, if we imagine a line that has-- let's see, these both have a slope of negative 3. These both have a slope of negative 2/3. So if you imagined a line that had a slope of positive 3/2 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 once again, I'm just eyeballing it. So a line that has slope of positive 3/2. 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, then this point would map to this point, which is what we want. And this purple point, negative 5 comma 5, 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 to this point right over here, this point would map to that point, and that point would map to that point. So a rotation also seems like a possibility for transformation C. Now let's think about transformation D. We are going from 4, negative 1 to 7, negative 3. Actually maybe I'll put that in magenta, as well. To 7, negative 3, just like that. And we want to go from negative 5, 5 to 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 to-- let's see, if I were to get from this point to this point, I could reflect around that, but that won't help this one over here. And 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 this point right over here. While this is rotating there, this point is going to rotate around like that and it's going to end up someplace out here. So that's not going to help. So it looks like this one can only be a translation.