Lesson video

Hi there, my name is Miss Darwish, and for today's maths lesson, we are going to be reflecting some shapes across both the x and the y-axis using coordinates.

But before we get started, if I can just ask you to take yourself to a nice peaceful area ready for today's lesson.

Okay, so the agenda for today is first of all, we're just going to recap on reflection and then we're going to be looking at the 4 quadrants and reflecting shapes across all 4 quadrants.

And then at the end of the session, there will be a quiz for you to complete on today's learning.

So before we start today's lesson, you will need something to write with, just a pen or pencil, a sheet of paper or a notebook, and a ruler.

So if you want to go and grab those three things, we can start with the lesson.

Okay.

In front of us, obviously we can see we've got the x-axis and the y-axis, and then we can see we have an orange right angled triangle.

Now, can you spot or can you see where the line of reflection is? I want you to point to it when you've found it.

Okay, have you found it? Now, I want you to tell me, is this line of reflection, is it vertical or is it horizontal? So is this line of reflection vertical or horizontal? It is vertical.

Well done if you said vertical.

Okay, now looking at this shape closely, we can see the following 3 coordinates.

We've got -5,7, 5,4, and -3,4.

Okay, so if we were to reflect the shape, it would look like the shape that you can see.

So we can see just the first quarter -5,7 reflects to 7,7.

So what's changed between the original coordinate -5,7 and 7,7? Can you see that the x has changed, but the y has stayed the same? So the y has completely stayed the same.

Why is that? So the coordinates from -5,7 to 7,7, only the x changed, not the y.

Why did the y not change? Well done if you said because the reflected line is vertical.

Okay? Well done.

Okay, let's have a look at -5,4 and that reflects to 7,4.

Well done.

And then the last one, 3,4 reflects to 5,4.

So in all three of them, we can see that when we reflected the shape, when the points were reflected, the coordinates only changed for x, but not for y because our line of reflection happened to be vertical.

Okay, so now we're going to have a look at this shape here, and this time we're going to be.

Write down for me, first of all, what are the three points or what are the three coordinates for this triangle? So find the three vertices of the triangle first.

Once you've done that, I want you to just jot down for me what are the coordinates.

Okay.

Have you done that? So we've got 2,6, 2,9, and 4,6.

Well done if you said that.

Okay, now when we've translated, we can see first of all, before we talk about what happens when we reflected, sorry, not translated, reflected the shape, we've got a line of reflection.

Is it horizontal or vertical? Our line of reflection is horizontal.

Well done if you said that, horizontal line of reflection.

So we've seen the coordinates.

And when we reflected the shape, because this time, our line of reflection is horizontal, which coordinates will change and which will stay the same? Our line of reflection is horizontal, so it's similar to the x-axis, so the x-coordinates we're guessing will stay the same and the y will change.

Let's have a look.

Okay, so point 2,6 reflects to 2,4.

Can you see the points? What would you write? The x stayed the same and the y changed.

It went from 6 to 4 after we reflected it.

Let's have a look at the next point.

2,9 reflects to point 2,1.

Again, because our line of reflection is horizontal, when we reflected that point, it went from 2,9 to 2,1, the x stayed the same.

And then let's have a look at the last one.

4,6 reflects to 4,4.

Again, what happened? The x stayed the same.

Tell me, why did the x stay the same? Because our line of reflection happens to be horizontal.

Good.

Next, we're going to extend the y-axis.

You can see our y-axis now goes from 6 all the way through 0 to -5.

We now have four quadrants on our coordinate grid.

Let's put some shapes onto here.

We've got a pink rectangle and a right angle triangle, and we're going to reflect each shape through the x-axis.

Let's start with the rectangle.

We reflect it through the x-axis.

We can now say that the shape is here.

Now, if we look at any particular point on our rectangle, we know that it should be the same distance from the x-axis on each version of the reflection.

So let's take this point, it should be 1, 2, 3, 4 away, and this point should be 1, 2, 3, 4 away.

We can say that -3,4 has been reflected to -3,-4.

Now, have a look at those coordinates.

What do you notice is the same, and what's different? Okay, we can see that other coordinate's value on the x-axis, which is -3, has stayed the same, but the y value has changed.

Let's look at the triangle.

I've now reflected it through the x-axis.

Again, let's look at a particular point.

We've got 4,-3 has reflected to 4,3.

Again, you can see the x-coordinates have stayed the same and the y-coordinates has changed.

Now, let's have a look at this shape here.

First of all, we've got the point -3,-2.

What I'd like you to do is I'd just like you to write down all of the coordinates.

I've given you the first one.

I want you just to jot down all of the coordinates, all the vertices, the coordinates of the vertices of this shape.

I'll give you a few seconds.

If you just want to jot the coordinates down now, and then we'll carry on.

Okay, I'll give you five more seconds.

Okay, let's have a look.

So the first one we said, -3,-2.

Now, if we reflect this point -3,-2, it reflects to -3,2.

Can you find where -3,2 is? Put your finger there.

-3,2.

You found it? Okay.

So where is the line of reflection? I haven't told you the line of reflection is the y-axis or the x-axis, but what do you think and why? So I've given you one point, -3,-2 reflects to -3,2.

Okay, first question you're going to ask yourself is which coordinates stayed the same? Was it the x or was it the y? It was the x.

So our line of reflection, that means our line of reflection is the x-axis, and we can change that.

So -3,-2, if it is the x-axis, let's just double-check.

How many squares away is -3,-2 from the x-axis, our presumed line of reflection? It's two squares away.

And then the point -3,2, where your finger is at, the -3,2, sorry, is that also two squares away from the x-axis or the line of reflection? It is.

Okay.

So -3,-2, reflects to -3,2.

And there are the rest of the points.

So well done if you said it reflects onto the x-axis.

Okay, now, let's find something a bit more trickier for you to do.

A triangle has the coordinates 4,-2, 4,-5, and -1,-2.

A triangle is a shape with 3 vertices, okay? So 3 of the vertices, the coordinates of these 3 vertices are given to us.

They are -4,-2, say them with me, 4,-5, and the last one, -1,-2.

Okay, we know the coordinates of the triangle.

Let's read on.

When reflected upon an axis, doesn't say x or y, the reflected coordinates are now 4,-2, 4,-5, 1,-2.

We know the original coordinates and we know the coordinates after it's been reflected, but we don't know about the line of symmetry.

It says it's reflected on an axis.

It doesn't tell us if it's the x or the y.

What do you think? I'll give you a few seconds to have a think and read through the question again.

Okay, what stayed the same with the original coordinates and the reflected coordinates? What stayed the same? Was it the x or the y that stayed the same? So you've got the x in pink and the y in green.

So we've got -4,-2 became 4,-2, 4,-5 became reflected to 4,-5, and -1,-2 reflected to 1,-2.

So we can see which, was it the x or the y that stayed the same? The y stayed the same.

Well done if you said that.

So then, where is the line of reflection? Is it horizontal or is it vertical? It's vertical because the y-axis must have been the line of reflection 'cause the y-coordinates did not change, so it's vertical.

Okay, and we can see the example over here.

We can see the original shape and then the y-axis is actually our line of reflection.

Okay, well done on that.

Now it's time for you to pause the video and have a look at the independent task.

Give it a go, come back, and we will then go through the answers and you can mark your work with me.

Good luck.

Okay, hopefully you didn't find that too tricky and that was okay.

Let's go through the answers together.

Have you got something to mark with? Okay, so the question said, I'll read it out first, a square with the coordinates -5,4, 5,2, 3,4, and -3,2 is reflected on an axis.

Doesn't tell us whether it's the y or the x.

When reflected, -5,4 becomes -5,-4, and -5,2 becomes -5,-2.

They haven't told us about the other two vertices of this square, they've just given us two.

So where is the line of reflection, first of all? So part one, where's the line of reflection? So we know -5,4 becomes -5,-4 and -5,2 is reflected to -5,-2.

What stayed the same? Was it the x or the y? Well done if you said the x stayed the same.

So if the x stayed the same, where is the line of reflection? It must be a horizontal line of reflection and it must be the x-axis.

So well done if you said the x-axis.

And now we want to know where the other two 3,4 and -3,2, what the coordinates would be.

So we're expecting it to be -3,something and -3,something, because we know that the x won't change if our line of reflection is indeed horizontal on the x-axis.

So -5,4 reflects to -5,-4, 5,2 reflects to -5,-2, as the question tells us, and then -3,4 reflects to -3,-4, and -3,2 reflects to -3,-2.

Well done if you got those right, if you want to give it a big tick.

Sometimes it's nice to do a question then go back and plot it onto a coordinate grid just to see it actually visually.

Okay, well done.

So if you would like to, then please ask your parent or your carer to share your work that you have done today on Twitter.

Make sure they tag @OakNational and use the hashtag #LearnwithOak.

I would love to see the work that you did today.

Now, before I leave you, I just want to say a really, really big well done on all the learning that you have done today, you have worked so, so hard.

Now it's time for you to complete the quiz about today's lesson.

Good luck with the quiz.