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## Properties & definitions of transformations

# Sequences of transformations

CCSS.Math:

## Video transcript

- [Instructor] In past
videos, we've thought about whether segment lengths or angle measures are preserved with a transformation. What we're now gonna think
about is what is preserved with a sequence of transformations? And in particular, we're gonna
think about angle measure. Angle measure and segment lengths. So if you're transforming
some type of a shape. Segment, segment lengths. So let's look at this first example. They say a sequence of
transformations is described below. So we first do a translation,
then we do a reflection over a horizontal line, PQ, then we do vertical stretch about PQ. What is this going to do? Is this going to preserve angle measures and is this going to
preserve segment lengths? Well a translation is
a rigid transformation and so that will preserve both angle measures and segment lengths. So after that, angle
measures and segment lengths are still going to be the same. A reflection over a horizontal line PQ. Well a reflection is also
a rigid transformation and so we will continue to preserve angle measure and segment lengths. Then they say a vertical stretch about PQ. Well let's just think about
what a vertical stretch does. So if I have some
triangle right over here. If I have some triangle
that looks like this. Let's say it's triangle A, B, C. And if you were to do a vertical stretch, what's going to happen? Well let's just imagine
that we take these sides and we stretch them
out so that we now have A is over here or A prime
I should say is over there. Let's say that B prime is now over here. This isn't going to be exact. Well what just happened to my triangle? Well the measure of angle C is for sure going to be different now. And my segment lengths are for sure going to be different now. A prime C prime is going
to be different than AC in terms of segment length. So a vertical stretch, if
we're talking about a stretch in general, this is going
to preserve neither. So neither preserved, neither preserved. So in general, if you're
doing rigid transformation after rigid transformation,
you're gonna preserve both angles and segment lengths. But if you throw a stretch in
there, then all bets are off. You're not going to
preserve either of them. Let's do another example. A sequence of transformations
is described below. And so they give three transformations. So pause this video and think
about whether angle measures, segment lengths, or will either both or neither or only one
of them be preserved? Alright so first we have a
rotation about a point P. That's a rigid transformation,
it would preserve both segment lengths and angle measures. Then you have a translation which is also a rigid transformation and so that would preserve both again. Then we have a rotation about point P. So once again, another
rigid transformation. So in this situation, everything
is going to be preserved. So both angle measure, angle measure and segment length are
going to be preserved in this example. Let's do one more example. So here once again we have a
sequence of transformations. And so pause this video again
and see if you can figure out whether measures, segment
lengths, both or neither are going to be preserved. So the first transformation is a dilation. So a dilation is a
nonrigid transformation. So segment lengths not preserved. Segment lengths not preserved. And we've seen this in
multiple videos already. But in a dilation, angles are preserved. Angles preserved. So already we've lost our segment lengths but we still got our angles. Then we have a rotation
about another point Q. So this is a rigid transformation, it would preserve both but we've already lost our segment lengths. But angles are going to
continue to be preserved. And then finally a
reflection which is still a rigid transformation and
it would preserve both, but once again our
segment lengths got lost through the dilation but we will preserve, continue to preserve the angles. So in this series of after
these three transformations, the only thing that's
going to be preserved are going to be your angles.