Lesson video

Welcome to another video.

I am Mr Maseko, in this lesson, we'll be going through coordinates recap.

Now, this will be a recap of things that you should have already done in year seven.

So before you start this lesson, I want you to get a pen, a pencil and something to write on.

Okay, now that you have those things, let's get on with today's lesson.

Pause the video and give this a go.

Okay, now that you've paused the video, let's go through this together.

What path did you come up with to go from J to K? Well, to go from J to K, we go one step to the right and then two steps up.

So J to K was one right and two up.

Now, what about K to L? Well, K to L, that is two to the right and three down, so K to L is two to the right and three down.

Now, the second student, well, she says the point negative three, two, so this point, negative three, two, is the same distance from J, so from J as J is from L.

So from J to negative three, two is the same distance as from J to L, which is one down and three right, whereas that point is three up and one left.

In the next part of the lesson, we'll go through how to find other coordinates that are the same distance apart.

Before going through how to find coordinates that are all the same distance apart, let's go through what coordinates are.

Well, coordinates are used to describe a path on a grid called a Cartesian plane.

Now, the path is always from an origin.

Now, remember, we can't just draw a path from nowhere, so in order to describe a path, we have to start somewhere, and we always start from the origin, which is the central point of the Cartesian plane, which is the coordinate zero, zero.

Now, when you're stating the path, we always state the horizontal direction first and then the vertical direction.

So the coordinate of point K, which is the path from the origin to point K, well, if we look at this grid, well that is on negative one, one, but what does that mean? It means to go from the origin to point K, we have gone, so from the origin to point K, we have gone one left and one up.

One left, negative one, and one up.

So what's the coordinate of point L? Well, the coordinate of point L is one, negative two.

What does that mean? Well, we have gone one right and two down.

We always state the horizontal direction first and then the vertical direction, and this is how coordinates are always written, and all coordinates are, they describe a path from the origin.

So if we want to find coordinates that are the same distance apart, how can we do this? Well, let's take point J, but what's the distance from point J to the origin? Well, how do we get point J? We go two left and one down, so that is negative two, negative one.

We want to find another coordinate that is the same distance from the origin, so we've got to travel the same distances horizontally and also the same distances vertically.

But we don't have to go left, instead of going left, what can we do? We can just go right.

So instead of going two left, we could go two to the right, and instead of going one down, we could go one up.

And then we find that point, two, one, is also the same distance from the origin as the point negative two, negative one.

As long as you've got the same distance horizontally and also the same distance vertically, you're the same distance away from the origin.

Now, there are other points that are the same distance from the origin, can you figure them out? Pause the video here and give that a go.

Well, what points did you come up with? Well, the same distance from the origin as point J, instead of going two left and one down, well, you could just go two left and one up, and you've got two left and one up, what do you end up? You end up with the point negative two, one, that is two left and one up.

That's the same distance from the origin as point J is.

You could do the other way also, we could go two right and one down, and we end up with the point two, negative one, that's also the same distance from the origin as point J.

So in the next activity, you are going to be trying to find as many points as you can that are the same distance from the origin.

Pause the video here and give this independent task a go.

If you would like a clue, stay for an extra 20 seconds to hear a clue.

So if you don't want a clue, pause the video in three, two, one.

Okay, so the clue that you can have if you've got to first pick a point on this grid.

And we're going to go with the point three, one.

So what other coordinates are there that are the same distance from the origin as the point three, one? Give this a go.

Okay, so now that you've given this a go, what coordinates did you come up with? Well, we started with the point three, one, so we went three right and one up.

So three right and one up, so what could we have done? Well, we could have gone three right and one down to the point three, negative one, and that is the same distance from the origin.

Or, well, we could have gone three left and one up to negative three, one, or three left and one down to negative three, negative one.

Now, what do you notice? All these four points are all the same distance, what do you notice? Those four points make a rectangle, and that rectangle, the centre of that rectangle is at the origin.

So the centre of the rectangle is at the origin.

Now, are there other points that are the same distance apart from the origin as these four points? Well, if you take this rectangle and you rotate it 90 degrees, so we rotate it 90 degrees, those four vertices, so the four corners of that rectangle end up at these four points.

So they end up at negative one, three, one, three, one, negative three and negative one, negative three.

Now, it doesn't matter what direction you rotate it, whether you go clockwise or anticlockwise, you will see the vertices of the rectangle you started with end up in the same places.

So now we have eight different coordinates that are all the same distance from the origin.

Now, this is if we start with a rectangle where the horizontal movement was different from the vertical movement.

But what happens if the horizontal movement was the same as the vertical movement? So what would have happened if instead of going three and one, we went five and five.

Well, if we go five and five in either direction, so left and then up or right and then up or left and then down, and then right and then down, what shape do we make? Well, it's not a rectangle anymore, the shape we've made this time is a square because all those distances are the same.

Now, the centre of that square is still at the origin, but what do we know about a square? Well, if you rotate a square through 90 degrees, the vertices just end up in the same places.

So when we rotate this, this point, negative five, negative five, if we rotate that vertex through 90 degrees, it will end up here at five, five.

So if we start with a square, there are only four coordinates that will be the same distance from the origin, but if we start with a rectangle, there are eight coordinates that will be the same distance from the origin.

So what's the maximum number? Well, that would be eight.

So pause the video here and have a go at this explore task.

Okay, let's see what you come up with.

Well, we started at coordinate zero, zero and move right or left a certain number of spaces and then up or down a certain number of spaces.

All we know is that the sum of the two numbers in these boxes has to be what? So the sum of the two numbers in these boxes has to be six.

Well, what can you have? You could have four and two, so whether they go left to right, that doesn't matter, so we could go four right and two up, so all we know is that the sum of those numbers has to be six.

So, well, instead of going four right, you could go five right, if we go five right, then we've got to go one up.

Or six right, or five right and one down, and then what you should notice as you plot all the points is that that point moves around so it acts as a locus and it keeps moving around and you end up back where you started.

Now, that shape that you've just made, what is it? That is a square.

Those distances are the same, so you end up making a square.

So I hope this is what you discovered also, and if you want to share your work, ask your parent or carer to share your work on Twitter, tagging @oaknational and #learnwithoak.

Thank you for taking part in this lesson, I'll see you again next time.

Bye for now.