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CCSS Math: HSG.CO.A.4

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.