Lesson video

Hello, my name is Mrs. Buckmire and today I'll be teaching you about reflections.

Now first make sure you have a pen and paper.

If you have a pencil and ruler, that could be useful as well, but no worries if not.

So pause and make sure you have equipment.

Okay, and then for this lesson, remember, when do I want you to pause? Good, whenever I say so, but also whenever you need to for a bit of extra time.

And remember to rewind the video if you want to hear something again.

That often can help, let's begin.

So for the try this, I have ways to revise some work on coordinates and equation of the lines.

So I want you to tell me three coordinates that lie on the line with at least one off the grid.

So one off the grid, what I mean by that is you might see a coordinate that might be over here and that's off the grid because, well, it's not within the grid axis given, but it is still on the line L3 and same for L4, maybe L1 down here or L2 all the way up here, so at least one off the grid.

And then I want you to tell me the equation of the line.

So hopefully this is something that you have learned before.

I wonder where L3 and L4 would intersect a line with equation X=-19.

Hmm.

You finish A and B and you have a bit of time, maybe have a think about that.

Where do you think L3 and L4 would intersect a line with equation X=-19.

Pause the video and have a go.

Okay, so lots of different answers you could get.

So, let's say if I chose this coordinate here.

So, to lie on L1, this is.

So this could be.

I could choose here, which is -5 and positive 2.

5.

I could choose off the grid down here, -5 and -4.

Here are some options So, lots of different ones you could get.

And same for L2, L3, and L4.

So if you can pause and check.

Now, what I really want to know is what is the same between each line, right? And the coordinates that's on each line.

So, for the first row what do you notice the same? For the second line, the second row here, the answers, what do you notice the same? Good.

So, with L1 all of the coordinates in this line all have have X coordinate that are -5.

So the equation is L1 is X=-5.

What about L2? Good, All the X coordinates are 3.

So, X=3.

What about L3? On this line here.

Good, now we have all the Y values, remember? And make sure when you plotted it, it's X first then Y.

So, here all the Y values equal to 4.

So, the equation of the line is Y=4.

And L4? Excellent.

Y=2 is correct.

Do pause the vide if you need some more time to check those.

Or even if you got them right.

Okay, so if you're ready to go at the wonderin' part.

Hmmm, so, a line X=-19.

All the coordinates on that line the X value's going to be -19.

So if it's going to intersect with L3, where's it going to intersect at? What would be the X coordinate? Yeah, it's on the line X=-19.

So, it's going to be at -19 and the Y coordinate? Good, four.

So, intersect and What about L4 then? If you know that answer now, what would the answer be for L4? Excellent.

19 and 2.

Okay, I'm using GeoGebra which is a fantastic website where you can explore lots of different things and we're going to explore some work on reflection.

Now, this is my reflection line and I can actually move it, but I'm going to keep it here for a moment.

And if I put the image in, it will reflect the original object.

So, image, I can see how it's reflected.

What I want you to take not of is how this distance changes.

So, distance from this point to this line changes when I move this point.

So, what's happenin'? So, when I move closer to the line, what happens? Yeah, it gets closer.

When I move further away, it gets further away.

So this is what is important with reflection, okay? So, with reflection the distance from the reflection line is always equal.

So, if this is two, then that should further reflected.

This distance is also two.

So here we can see it's one, two, three, four, five, six away.

So the reflected point is one, two, three, four, five, six away, okay? So, that's what's important when we're reflecting.

Okay? Now, you can also see, so, if I move the line of reflection.

Let's do that, let's move it, like, here.

You can see it get further away, because I'm getting further away from my object.

So, the image also has to get further away.

Ahh, it's off the screen.

Okay and what about if we move it past the line? What do you think is going to happen? Whoa, there we go.

So now, it's two away.

It's still two away, okay? So even when you go past, we can make some really cool patterns here, it would still be equal distance from the line.

Now, this also holds true with diagonal lines, okay? So let's do a slightly smaller triangle to look at.

Let's see if I can.

Here we go.

Okay, so we can see that actually, even with the diagonal lines, it still reflects.

And I could actually change this in lots of different ways, but it's still going to be equal distance.

So, if we see, let's do.

Let's do it like this so it's at the point.

So, here it's zero away from the mirror line and that other point is also zero away.

Here, it is, like, one and a half.

So this point is, like, one and a half.

So, pretty exactly on there.

If I can draw it to help show it.

So, here it's one and a half and so on the other side it's a half and one.

So exactly the same distance.

Here it's one and this distance is one.

So, it even holds true when you are using diagonal lines of reflection as well.

Okay, so from that GeoGebra we're just seeing reflections is a type of transformation where moving our object from the image.

We can reflect shapes in the line of reflection.

The size and shape remain the same, but the shape is flipped over the line.

Points and their reflections will be equidistance from the line of reflection.

What does equidistant mean? Good, equal distance.

You can almost see it there.

So equidistant from the line of reflection and you can see in this diagram here how from the object, while the object vertex here is two from the line, so the image is going to be two away.

And here it is two, four, six from the line.

So the vertex image is two, four, six away.

So may you pause this and add this to your notes.

Okay, T an U are reflections of S.

So that means S is our object and T and U are images and we want to find the lines of reflection.

So, the way that I would do this is I would choose corresponding vertices.

Maybe this one and this one for T and then seeing actually what's the distance between them and then finding halfway.

So here, there's one, two, three, four.

So halfway, actually, you've already got a lovely dot is that line of reflection.

And you can do the same for U.

So that's how I would find lines of reflection.

Then, I want you to kind of go a step further.

I want you yo explore the effect on the reflected images, if it's translated, if S is translated by the following vectors, okay? So let me explain what I mean by that.

Let's rub these out, 'cause we don't need this.

Okay, so if S is translated by , do you remember vector notation? What does mean? Good.

One's based to the right.

So one's base, so it's getting closer or further away from the line of symmetry? The line of reflection, sorry.

Good, it's getting closer to the line of reflection.

So, each point moves one to the right.

So, what do you think will happen to T? Remembering that the line of reflection, it's always that each point is equal distance away.

So, here's zero, so now that point is going to be zero as well.

So, how will it move? So, even better if you can think about how it is translated and write it as a vector.

Similarly for U.

So, U's down here at the moment if S moves, how will U move? How will it be translated? So, write in that notation as well.

And then you can try it from and.

So, it could be useful to do a little sketch or just have a little think about, oh what do I think will happen? Where do I imagine it will move? That's fine as well.

So do pause the video and just have a little go at that.

So I hope you've had a chance to have a think about those.

I just want to use GeoGebra to just show it live what's going on.

So, I am, I just love GeoGebra cause it's so dynamic.

So we can see with S, when I move one to the centre.

Oh look, one to the right, T gets closer.

So T goes inward.

So T was here, and when S gets closer, T gets closer.

So what would that be in vector notation? Fantastic.

It's moving one to the left, so.

What about U? Good job, U moves the same as S, it moves one to the right.

Interesting.

Okay, so, the first one was.

So T went to the left and U was.

Oh, I haven't said what the lines of reflection were, what were they? Do you see them? Okay, so this one.

So, we have to mash and point, so we have this coordinate would be.

This coordinate would be.

So it seems like our X=5.

And this one, so here we have.

Here we have.

Ah, so it looks like Y=3, awesome.

Okay, so, let's see from.

So if S moved.

So imagine you've got that tool where we can just shift S up by one.

So S is moved up here, what will it effect? Will if effect T or U? Both of them? What did you get? Good, it will effect them both.

So, U will actually move further away, 'cause it's moved further away from the line here.

So, it's two away so now that will be two away.

So everything's moved down by one is the difference.

So what's that as a vector? Excellent, 'cause it moved down.

So, what about T? How will T change? Good, it will actually also move.

So actually, the same as S.

Hmmm, interesting.

These are the same and this one these are the same.

Okay,.

So what does that mean, first? So, one to the right, ah, and one down.

So one to the right and one down.

So, one to the right.

Can I do this in green? Left.

One to the right and one down.

One to the right and one down.

So looks like it's going to be, like, here.

So I hope this is clear enough for you.

So, boom, boom, boom.

Here we go right here.

So, now, actually T is also going to move.

T's going to move to here.

So it's moved one to the left and one down.

So, one to the left, how would that be written? Good, -1.

And one down? 1.

And what about U? Excellent, so U will actually be moved that way.

So, it's going to be moved one to the right and one up.

So one to the right is 1 and one up is also 1.

Really well down if you got those correct.

Okay, so now I want you to have a go with the independent task.

So, describe the following transformations from A to B and B to D, A to C and C to B.

Warning, they're not all reflections.

I put transformations because I just want you to have a little practise with something that I'm hoping you've done before.

This page one of two.

And page two of two, reflect the octagons E, F, and G, and H so that they form a tessellation inside the square.

Describe the four reflections.

Okay? So that's a little challenge, but I thought it'd just be a bit of fun rather than just reflecting.

Normally, you'd have to try and create something.

So create.

So, tessellate.

So, tessellate means that they don't overlap.

They fit exactly without any spaces and then describe the four reflections.

Pause the video and have a go.

Okay, so describing our A to B.

So when you describe, we're going to.

We want the line of reflection to be exactly halfway, so we're going to count halfway between them.

So, here, we have one, two, three, four between them.

So the line's going to be like this.

It should be a straight line, it should be like that, really.

And we'll call it.

So think about.

Imagine coordinates on there, what would it be? So , ,.

Ah, X=1, then.

So as reflection in the mirror line X=1.

What'd you get for B to D? Good, it was also a reflection.

Reflection in the X-axis.

A to C? Yeah, reflection in the.

It should be X-axis, as well.

And what about C to B? Ah, this was a trick one.

What did you get? It was a rotation.

Rotation, about 180 degrees.

Really well done if you got that.

It was not a reflection, it was a rotation.

Okay, so for reflecting the octagons, I put a little image here to show you how I reflected it.

Now there might be another answer, I'm not sure, but this is the one that I got.

And the four reflections.

So, E is reflection in the mirror line Y=9.

F is reflection in the line X=9.

G is reflection line Y=5.

And H reflection in the mirror line X=5.

So, do pause and just have a quick go and check at that if you did not agree with it.

Okay, so, for our explore task, it's a bit of a challenge, but I think you're up for it.

There are four copies of the triangle shown here.

So it's 2 and 1.

And they're arranged as follows: They're arranged with A, B, C, and D.

And what I want to know is, describe the transformation from B to C.

Describe the transformation from C to D and describe the transformation from D to B.

Okay? Now, maybe have a little go, I'm not going to give you any hints yet, they'll be support in moment.

But maybe just have a little of the problem and think what do I know? What can I find out using what I know? So, given the information, what else can I find out and then have a go at describing, but first, take that time to really add to the diagram and find out and put all the information you have on the diagram, 'kay? Okay, page support.

So when I said, "oh, put everything on the diagram," what information do you think I meant? So is this, is it the fact that it's 2 and 1? So we know this is 1, and this is 2.

So if we know that, then we know this vertex and we know this vertex as well.

Because if this is.

Then, well, this is going to be.

What changes the X or Y? Good, because it's long, so it's going to be X value that changes.

It's going to be one to the left of it, so it's going to be -3.

And the Y value too is still going to be parallel to the Y-axis, to the X-axis, sorry.

So, it's going to be as a coordinate.

What would this coordinate be? Excellent.

It's going to have the same X value as the one we just found, so -3, but it's up two.

So, it's going to be.

So, what I challenge you first do is go around and just find all the missing coordinates using a bit of reasoning.

And then, try and think about what would the transformation from B to C be et cetera.

Okay? Pause the video and have a go.

Okay, so hopefully you had a little go at that.

So, for this one is one that we already did.

So, and Now, so what's it going to be? Good, it is a reflection and they're not all reflections, by the way.

Well, maybe.

So it can be a reflection here.

So, what is halfway between them? This one is this one being.

Oh, nope.

.

So halfway between and is going to be is the point here.

So that line, the line of reflection is X=-4.

So, it's reflection in the mirror line X=-4.

Well done if you got that.

Okay, so here what we can see is it looks like a reflection again in somewhere here.

So, I've labelled all the vertices.

So now we go to , so what's halfway? Good,.

So it looks like it's going to be the Y value.

And the Y, it's horizontal, so it is the Y.

So, it's Y=2, is halfway.

So it's reflection in the line Y=2.

Well done if you got that.

Okay, and finally from D to B.

Hmm, now there are some different answers to this, but the one that came up to me first, so I'm going to do that one, is if we know that B, so this one, we just did that wasn't it? It was and this one was.

Oh, sorry.

I don't believe it.

.

What was this one?.

Okay, and that's.

So, this point here is going to be.

Um, and we have, and this one then is.

Whoops, why's this not working? Okay, so I'm kind of starting to plot points around it.

And this one was.

So, we can see that this point here is actually going to be and I can see actually it looks like.

So that's a diagonal and that's a diagonal of, like, one square kind of thing.

So, it looks like actually it would be a rotation.

So it could be a rotation.

About 180 degrees.

Could've been movin' and it was originally down here and it's being turned all the way around to there.

Well done.

Really well done if you got that.

You know I like to throw in a bit of a curve-ball there.

Now there is though, um, there might be another way, bu they're the ways that I found.

So just check yours carefully if you think there are.

Really, really well done today everyone.

If you had a go at the try this and you had a go at the independent task and the connect task, even, as well.

I think you've done a sterling job.

You should be very proud of yourself.

I'd love you to write down the key things you think you need to remember from today's lesson and then have a go at the exit quiz.

'Cause that's a really ideal opportunity for you to test yourself and just show off what you've learned.

Have a lovely day.

Bye.