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# Determining mappings (incl. dilations)

Video transcript

Perform transformations on
the movable quadrilateral until it matches
quadrilateral NEUT, quadrilateral NEWT
right over here. Are the two figures congruent? So we have our
little tools here. But I'm actually going to
do it on my scratch pad first to think about how we
might want to transform it. So the first thing-- it looks
like this point right over here would correspond to point E
once we shift it over and then maybe dilate it down and
then reflect it over. So let's try to do that. So the first thing, if
we were to translate, so how much are we
going to translate by? So we're going to move
to the right by 1. So in the x direction, we're
going to increase by 1. And in the y
direction, we're going to go up by-- we're going
to go from negative 4 to 1. So we're going to
translate by 1, 5. So that's going to put
our figure like this. So that point is going
to be right over here. Everything is going to go
in the x direction by 1, and then 1, 2, 3, 4,
5 in the y direction. So this line is going
to look like that. So 1, and then 1, 2, 3, 4, 5 is
going to go right over there. So that's going to
go right over there. I'll try my best to draw it. And then 1 in the x
direction, and then 1, 2, 3, 4, 5 in
the y direction. So it's going to look
something like this. Or it's going to
look like this right after that transformation. And now, what we
could do-- let's see, we could either
reflect first, or we could try to scale
it down first. So let's try to scale it down. Let's try to dilate it. So let's dilate it. And let's make our center. I don't want to change
this point right over here. I like it sitting
there because that seems to be the point
that it corresponds to. Let's put the center there. So let's put the center
at the point 5 comma 1. So the center is going
to be right over there. And we essentially want this
line, which has length 6, to be scaled down
to have a length 3. Or essentially, we
want this point right over here, which is 6 to
the left of this point-- we want it to be 3 to
the left of this point. So we want it to
get half as far. So we want to scale by 1/2. So then that's going
to get the figure-- this point is going
to be over here. This point, which is in
the y direction, 2 away, is now going to only be 1 away. Let me make it clear. In the x direction, it sits
at negative 3 relative to 5. So it's 8 away. So now it's only going to be
4 away after a scale of 1/2. In the y direction, it's 2 away. So now, it's only
going to be 1 away. So that point is going
to go right over there. And then this
point-- or actually, let me focus on this
point right over here. We're not looking
up there just yet. This point right over here,
in the x direction, is 4 away and, in the y
direction, is 4 away. So at a scale of 1/2
in the x direction, it's now going to be 2 away. And in the y direction,
it's going to be 2 away. So it's going to look like
this after the scaling. And now it looks pretty clear. We just have to do a
reflection around this line. We just have to do a reflection
around the line y equals 1. Reflect around the
line y is equal to 1. So let's do all of that
on this actual tool now. So first, I did the translation. I'm going to translate
in the x direction by 1 and the y direction by 5. That got me right over there. And then I wanted
to dilate it down. So let me scroll
down a little bit. So dilate it about
the point 5 comma 1. And then by a scale of 1/2. So that scaled me down. And now I'm going to
reflect over y equals 1. So I'm going to
reflect over the line. Well, the line y equals 1,
it goes from the point 0-- I'm just picking
two points on it-- so it goes from the
point 0, 1 to 1, 1. And there we have it. We've gotten to that point. Now, we have to
answer their question. Are the figures congruent? Well, no. The first figure was much
bigger than this one. And the way that we got it to
be able to squeeze into this one is that we dilated it down. These figures would
have been congruent if all of my
transformations were just translations, reflections,
and rotations. But I had to dilate it. I had to scale the figure. Because I had to
scale the figure, these figures are not congruent. No, the figures
are not congruent.