ontrack-media.net/.../GM2L6.mp4

[silence]

So I heard you didn't really

get the transformations,

but I think I can help you

out a little bit.

So, transform just means

change something.

You already know that.

And in geometry,

there are some
types of transformations

that are helpful to know about.

So, the main thing is

you have a first thing

and then a second thing.

So, one shape changes

into another shape.

And, the first one's called

the pre-image,

and the next one's
called the image.

So, "pre" just means before.

Just remember that,

like pre-liminary and
pre-historic

and then the next image.

So, the first kind

is a reflection.

And again, you know what
this means already,

but a reflection in geometry

just means that

you've flipped something

over an axis.

So, you could even look

at your hands.

This hand is a reflection
of the other hand.

So, they've just flipped
onto each other,

or you could think about a

um, like a landscape scene.

If you look at a lake

that's reflecting,

like the mountains,

then it's just,

the axis is that line

of where the lake starts.

So, that's a good way
to remember.

Another kind
is called a rotation,

and you know what that is too.

But a rotation just means

you're switching a shape

onto a rotating axis.

So, like this.

And, another way to think

about a rotation

is two reflections.

And, that doesn't need

to be confusing.

All you need to know is that

if you have one thing

reflected onto another

and then it reflects again,

it ends up being a rotation.

So...

That's a good way to
remember that too.

And, one more type

is called a translation.

So, this is just like a slide.

So, just like this

moving over here.

That's a translation.

Another way to think

about a translation is again,

two reflections,

but this time the reflections

are in a straight line.

So, if you reflect
this hand...here

and you reflect it
one more time,

then this hand

has reflected over here.

So, sorry

this hand has translated
over here.

So, these types, um,

of transformations
are called isometric.

A translation, a rotation,
and a reflection

are all
isometric transformations.

That just means same.

So, when you start out

with a pre-image,

it will always be the same size

and shape as the image.

But, there's one more type

of transformation

that isn't isometric,

and that's called dilation.

And, if you ever go

to the eye doctor,

and they dilate your eyes,

it means they made them

really big so that they could

see inside them.

So, when you dilate a shape,

you make it either

smaller or bigger,

one of those two.

So, one more term

is a glide reflection.

And a glide reflection

is exactly what it sounds like.

It's just one reflection

plus one translation,

and these can be
in either order.

You could either
translate and then reflect

or you could
reflect and then translate.

Either way.

[pause]

So, transformations are helpful,

because we can know about

something called a tessellation.

And a tessellation is

just a repeating shape,

but only certain types
of shapes can repeat

in patterns that don't overlap.

So, if we had like

a crazy star or something,

it wouldn't tessellate,

because it's a weird shape.

But, if we had just like
a square or a rectangle,

it'll tessellate perfectly,

because they can overlap

in any sort of pattern.

So like, it's why we can have

a brick wall or something,

you know.

They can...

they perfectly fit
next to each other

and on top of each other.

But, if you need to know

what types of shapes
can tessellate,

we can remember
by angle measure.

So, if all the angles of a shape

equal 360 degrees,

then they'll be able
to tessellate.

So, sometimes you can look

at a shape and figure it out.

Other times, maybe you can't.

So, if you need to remember

what types of shapes can,

if all the angles that meet up

equal 360,

then you're in business.

You can tessellate.

So, you know rectangles can,

like in this picture.

But then in the next one,

we have two different shapes.

We have squares and triangles,

and you can see that

all these angles together,

the 90 plus 90 plus
60 plus 60 plus 60

equals 360 degrees.

And, if you just add up

all the angles that touch

and they equal 360,

then you can see,

like right here,

that they tessellate perfectly.