Lesson video

Hi there.

My name is miss Darwish and for today's masters, we are going to be trying to find the coordinates of a shape after it has been reflected.

So before we get started with the lesson, if you could just take yourself to a nice quiet place ready to start.

So the agenda for today's lesson is first of all, we're going to be looking at finding missing coordinates.

Then we're going to be having a look at some reflections and then we're going to be putting the two together.

So we're going to be looking at missing coordinates after a reflection has happened.

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

So, to begin the lesson you just need a pencil, sheet of paper or a notebook and a ruler.

If you want to go and grab those things then we can stop.

Okay.

Ready to start? So, missing coordinates first of all, the point marked in front of you has the coordinate seven minus two.

I want you to get that finger and put it on that point, seven minus two of the coordinates.

So what does that mean? That it has an x of seven an x-coordinate of seven and a y-coordinate of minus two.

Good.

So the x is positive and the y is negative because it's in that fourth quadrant.

Okay? And in that fourth quadrant, the x is positive and the y is negative.

So seven minus two is that point.

Now, you can take your finger off.

This point is actually one of four vertices of a rectangle.

So a rectangle is of course a quadrilateral, which means it has four vertices, well done.

And I have shown you one of them and it has the coordinates seven minus two.

Okay? Now I'm going to show you the other three.

Here are the other three.

Can you make out a rectangle? Yeah.

Okay.

So I've shown you the black coordinate.

You know what that coordinate is? Okay.

There are four vertices.

We only know the coordinates of one of them.

Seven minus two.

Now, I'm going to give you some thinking time now.

Okay? If you want to jot down notes on your notebook or your sheet of paper, go for it.

What do we know about the other three coordinates, the other three vertices? Do we know any of the coordinates? Just from the information that you have so far? Let me give you a few seconds to have a think.

And like I said, if you want to jot anything down, feel free to.

So what do we know about the other coordinates? Okay.

Hopefully you've had some thinking time and maybe gathered a few ideas.

Should we go through these together and see what we can come up with? Okay.

So, what do we know about this one? We know it has a y minus two, the y-coordinate is minus two because it's in the exact same position.

The y, it will have the same y as the seven minus two as the first one.

Can you see that? We can see along the y-axis, we know that.

So just by the beginning of the question, let me just go back.

We were told that that point had the coordinate seven minus two and the first thing we would do, a question like that is grab your pen or a pencil and automatically write on the x-axis and the y-axis, the information we have.

So for the rest of the question, things will be easy for us to figure out.

Okay.

So, back to this.

We know that that has a y of minus two, we can see that on the y-axis can't we? Okay.

Do we know anything about this point? What do we know? What don't we know? Do we know the x? We don't have enough information.

Do we? What about the y? You don't have enough information for that one either.

What about this one? We know it has an x-coordinate of seven.

Follow it down on that x-axis it crosses at seven.

And what about the y-coordinate? You don't have enough information.

So we know the x but not the y.

Okay.

Let's have a look at another question.

So, the coordinates of two vertices are written below.

So first of all, can you see a quadrilateral? point at it.

Brilliant.

And it has full vertices A, B, C and D.

Now, we know the coordinates this time of two of those, B and C.

What are the coordinates of B, tell me? Five minus one.

Well done.

What are the coordinates of C? Four minus five.

Okay.

I want you to put your finger on B and say five minus one.

Now I want you to take your finger and move it to C and say four minus five.

Okay, you can take your finger off now.

Right.

So let's carry on with the rest of the question.

Reflect the shape on the y-axis first of all.

That's the first step they want you to do.

So show me, is this the y or is this the y? This is the y-axis.

The y-axis is a horizontal vertical line.

It is a vertical line, well done and we need to reflect or flip the shape onto the y axis.

Okay.

There it is.

If it's reflected.

Okay.

Now we're just going to rename it before we move on any further.

Okay? So we've reflected it.

Of course, if A is closer to the y-axis, then A dash is reflected point.

So, A dash is the reflective point of A, B dash is a reflective point of B, C dash is reflective point of C and D dash is reflective point of D, well done.

So, we've reflected the shape now.

So, because A is closer, A and C are closer to our mirror line or our line of reflection, then A dash and C dash also have to be closer to the line of reflection.

Good.

Okay.

Now the question is asking, what are the coordinates for A dash and D dash? They didn't give us the coordinates, notice how we didn't get the coordinates for a A or D, the original points but now we need to work out the coordinates of A dash and D dash.

Okay.

What can we do? Have a think first, before we go through it together, what can we do first? What's the first step we can do.

Okay.

Let's look together.

So step one, write what we know.

Do you remember when I told you that before? You grab your pen or your pencil and on that x and on the y we're going to write what we know What do we know so far about anything? We know the coordinates for point B because they are five minus one, or we know the coordinates for C because they are four minus five.

Well done.

Okay.

So, I've marked on the y-axis so we know where minus one lies on the y-axis because of point B.

Can you see that? And because of C we know where minus five would lie on the y-axis.

And of course they would be below zero.

Okay.

Guess what the next step will be? We've written, we've marked out Ys, our y-coordinates on the y-axis now we need to mark our exes.

So, because B has a coordinate five minus one, we know where five would be on the x-axis.

And we also know where four would be because of the coordinates C.

Right.

Now we've got our markings.

We know where four and five are on the x-axis, and we know where minus one and minus five on the y-axis.

Brilliant.

Okay.

So have we done step one? Has step one been completed? Yes.

What is step one? We write what we know.

Whatever information is given to us in the question, put it on that sheet of paper.

Write out, Mark on the x and the y-axis.

Okay? That's how I like to work things out any way I have to see it Right.

We're ready for the next step now.

So, just to recap first of all, if we reflect to shape onto the y-axis, then only what coordinate stays the same? The x stays the same, or the y stays the same.

If we reflect onto the y-axis, what stays the same? Tell me, shout it to me.

I can't hear you.

Shout it.

The Y coordinate stays the same.

If we reflect on the y the y-coordinate stays the same.

If we were to reflect on the x, then the x-coordinate would stay the same.

But in this question, our mirror line or our line of reflection is the, the y-axis Okay.

Let's go back to the question now.

So we've got our markings.

Okay.

What might step two be? Have a think and tell me.

Okay.

Step two now, right? Let's see if you're right.

So point A, we know has an x of four, when we reflect onto the y-axis, A dash becomes minus four.

Okay.

So the only, before when we were recapping, let me just go back a bit.

We set the y-coordinate when we reflect stays the same, the x-coordinate almost stays similar.

The digits stay the same, but it goes from positive to negative or from negative to positive.

Okay.

So four becomes minus four, five would become minus five.

We're talking about the X axis.

The one that does change.

So A is four, A dash would be minus four.

If B is five, B dash would be minus five.

See how easy that is.

Maths is easy.

Okay.

So, now that we've done that, we know the y-coordinates are going to stay the same, and we have the x for A dash and C dash, and we also have the x for B dash and D dash.

So for B, the coordinates were five minus one, which we knew from the question and C the coordinates four minus one which we knew from the question.

So now we've got A dash, would be minus four minus one.

Can you see that? Want you to put your finger on A dash, read the x-axis, the x coordinate on the x-axis minus four and the y minus one.

And then now put your finger on B dash, what's the x-coordinate? minus five.

Move your finger along on the y, minus one, well done.

And then C dash, put your finger on C dash, found it? And read the x-axis, minus four, and move your finger along what's the y-coordinate? Minus five, and then move your finger to D dash and do the same.

What's the x-coordinate for D dash, minus five minus five.

Okay.

You see how we, worked that question out just in two steps.

Always, always write what you know on the x-axis on the y-axis.

And then think if you're reflecting on the y-axis, the y-coordinate stays the same.

If you reflect on the x-axis, the x-coordinate stay the same.

Okay.

Well done.

So now it's time for you to pause the video and have a go at the task that I've got prepared for you Have a go check your work, and then come back and we and you can mark your answers with me.

Good luck.

Okay.

Welcome back.

Hopefully you found that okay and not too tricky.

Should we go through the answers together? If you've got a pen or something to Mark with, you want to go and grab that and we can have a look.

So, the task that I left you with looks like this.

And it said, so there was a triangle.

And, we have the three vertices, A, B and C, And it said the coordinates of A and C are given.

Write down the coordinates for B dash when the shape is reflected onto the y-axis.

So first of all, the coordinate for A is eight nine, and the coordinates for C ten seven.

So what was the first that we should have done? Mark them on the x and the y so well done if you did that.

So we know that A has an x of eight and a y of nine, and C has an x of 10 and a y of seven, and then B, we could work out based on A and C.

Now we are reflecting the shape also onto the y-axis.

That's important to remember, because that tells us that the y-coordinates don't change.

So, first step, hopefully you've got your markings on your sheet.

So we know that the y nine and seven should be marked like that.

So in the first quadrant, cause it's all positive.

So B would have a y of seven and a nine, of course, as it says, and then the x-coordinates also should be marked with eight and 10.

So well done.

If you did that, I'm just going to ask you to give yourself a nice big tick just for completing step one.

Okay.

So well done if you wrote everything down.

Okay.

So we've got B and A, have an x-coordinate of eight, C has an x-coordinate of 10, B and C have a y-coordinate of seven, and A has a Y coordinate of nine.

Okay.

Let's move on.

So B then, the coordinates for B would be eight 10.

Now, if we are going to reflect onto the y-axis, then our shape would look like this.

So points A and B will be closer to the y-axis.

Sorry, points A dash B dash would be closer to the y-axis.

Just like points A and B are So, there's A dash, B dash and C dash.

Hopefully you did your markings as well.

Now, B dash is what we were asked for and the coordinates of B are eight seven.

Which coordinate is it? Because we're reflecting on the y-axis, doesn't change, the y-coordinate.

So B dash will have a y of seven and the x, the sign will change or go from positive eight to negative eight.

So the answer to B dash would be negative eight seven.

So remember that we're reflecting on the y-axis, the vertical line.

So because we're reflecting on the y-axis, which coordinates stays exactly the same? the y-coordinate does, well done.

And what happens to the x-coordinate? The actual digit stays the same but the sign changes.

So if it's positive, it becomes negative.

If it's negative, it becomes positive So eight became minus eight.

Give yourself another really, really big tick.

If you also got that.

Okay, well done.

If you would like to share your work with us here at Oak National, then please ask your parent or your carer to share your work for you on Twitter, tagging @OakNational and #LearnwithOak.

Just want to say a really, really big well done on all the learning that you have done today.

You have been brilliant and you should be extremely proud of yourselves.

Now it's time for you to go and complete the quiz.

Good luck.