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Welcome to our fourth lesson in the coordinates and shapes unit.

Today we'll be solving practical problems involving coordinates.

You will just need a pencil and a piece of paper for today's lesson, pause the video and get your equipment if you haven't done so already.

So here's our agenda, we'll be solving problems involving coordinates starting as always with a knowledge quiz to test your learning from the previous lesson, then we'll be looking for patterns in coordinates, we'll be finding missing coordinates, and then you'll work on some independent learning before completing a final quiz to test what you've learnt in today's lesson.

Which we'll do now.

Sarah has identified the plotted points but some of them are incorrect.

Can you correct her errors? Pause the video while you do so.

So for the first one, you will have seen that A, is in the top left quadrant and we know that coordinates in the top left quadrant have a negative x coordinate, negative X coordinate and a positive y coordinate.

So we know that her two six is definitely incorrect.

So we go along the x axis, it's minus six, up to the y axis, it's a two, so this should be.

For B, we know that there should be negative x and negative y.

Well, it is.

But you can see that she's looked at where the x coordinate is, which is halfway between minus two and minus four, but that's minus three.

So she's read the scale incorrectly.

It's minus three, and halfway between minus four and minus six is minus five.

For C, we know that this is on one of the axes so one of the coordinates will be a zero.

If we go along the x axis, we can see that it's at zero on the x, and if we go up to the y axis we can see it's at five, so this one is correct.

So D, she's only actually put one coordinate.

So we go along the x axis, it's up to eight, but we can see why she's missed one off, because it hasn't gone up or down the y axis is a zero on the y axis.

So she needed to put the zero in because you always have to have a coordinate for both the x and the y.

The E, we see that this is in the bottom right quadrant, so it should be positive x, negative y.

So we go along to nine and down to minus eight.

So she did the y coordinate first.

Remember, we always go along the corridor, and up or down the stairs.

So now let's look for some patterns in coordinates.

I'm going to plot the point , and then the point , and join them with a straight line.

So what I've made here with a horizontal line by joining these two coordinates, and I need to see what do I notice about these two coordinates, so I can see that they have the same y coordinate.

So if I look at a horizontal line, the line is horizontal, because it is in the same position on the y axis all the way along.

So therefore every point along this line will have a y coordinate of two, because it hasn't moved on the y axis.

So I'll check that, I'll look at this point here.

This is minus three on the x axis, and one, two on the y axis.

Let me check another one here, this is one on the x axis and two on the y axis.

So if we look at the points all the way along this line, their y coordinate is always two.

That tells us that all horizontal lines on a coordinate grid have a constant y coordinate.

Wherever you see a horizontal line on a grid, the y coordinate will always be the same.

Let's have a look at another pattern here.

So I've drawn the point So I've plotted the point and draw a vertical line through it.

Now I want to think about what will the coordinate pattern be on this line.

So pause the video and make some notes about coordinates down this vertical line.

So we can see that this one was , let's have a look at another one.

This one here is minus one, minus two, minus three, minus four on the x axis and minus one on the y.

Let's have a look at one more.

This one is also minus four on the x axis, and it's at minus three, on the y axis.

So we can see that on this vertical line.

Each x coordinate is minus four, because its position in relation to the x axis has not changed.

Therefore, we can state the rule that vertical lines have a constant x coordinate.

This is important to remember, so horizontal lines have a constant y coordinate, and vertical lines have a constant x coordinate.

Now let's apply this to shape.

So a square is drawn with one vertex at point I'm going to mark that on there.

So if we look at the horizontal lines here, we remember that horizontal lines have a constant y coordinate.

So we can see that the points on the horizontal line up here will have a y coordinate of two.

So the points on the horizontal line will have a y coordinate two or this is a horizontal line as well here, their y coordinate here will be minus two and this will be Something minus two.

Okay? And then we know that all vertical lines have the same x coordinate.

Therefore all of the points on the vertical sides for x will either be minus four, or zero.

So this one will be minus four because this has the same x coordinate as the one above it, and these two are on zero on the x axis.

So they will be.

So we can see the pattern here about the constant x and y coordinate in vertical and horizontal lines.

Let's now look at what else we notice about the difference between the coordinates.

So if we look at the top horizontal line, the x coordinate is minus four on this vertex, and zero on this vertex, the difference between those two is four units, which tells us that this shape is four units wide.

If we look at the difference on the vertical line between the y coordinates two and minus two, the difference is four.

So that confirms that this is four high.

Is a square, so all of the sides are the same shape.

Now looking at the difference between the coordinates helps us when we're dealing with a missing coordinate, so that we can figure out the length or the width of a shape.

Let's have a look at one more I'd like you to pause the video this time and generate some statements really reasoning about the coordinates in this rectangle and cay you mention the coordinates on the horizontal and vertical lines, and then the differences between the x and y coordinates.

So we know that the horizontal lines will have the same y coordinates.

So that horizontal lines we've got here, this one is at And we're going to just look at the forget about the x for now we're just thinking about the y we know the y coordinate is the same, so it's going to be three here.

Okay, now, here we've got the vertical line, we know that the vertical lines have the same x coordinate.

So the x coordinate for this vertex is going to be one.

And then we can look at the y coordinate is minus one.

And then we can label this one as and this vertical line here will have the same x coordinate as this one, so it's.

Now I asked you to look at the difference between the x and y coordinates, you could see that here looking at the x coordinates, one and three has a difference of two, which tells us that the shape is two units wide.

And the y coordinates, three and minus one have a difference of four, which tells us that the shape is four units high, we're going to be using this detective work to find missing coordinates.

So now I've got three vertices of a square plotted at the points indicated on the coordinate grid.

And I need to find the coordinates of the missing vertex.

So it's always good practise to annotate the known vertices.

So I'm going to start up here, I've got , and I've got And this is on a vertical line.

So I knew that they were both going to have the same x coordinate, these are in a horizontal line.

So they're going to have the same y coordinate.

So this is going to be something minus six the same as this one, and it is.

Now I can use my knowledge of horizontal and vertical lines to help me, I know that the missing vertex, which is going to be somewhere here, is going to be on a vertical line with this one.

Therefore, it's going to have the same x coordinate, which is minus two and I know it's on a horizontal line with this one, so it's going to have the same y coordinate of two.

So my missing vertex is at.

Another way I could have looked at it was to think about what is the height and the width of the shape.

So using my known vertices, I can look at the difference between the y coordinates two and minus six has a difference of eight.

So I know that the height is eight units.

And here I have the grid to check, one, two, three, four, five, six, seven, eight.

Okay? But you won't always have the grid that's why we have to learn how to do it this way.

And then I'm looking for the width of the shape, so I'm looking at the difference between the x coordinates on my horizontal line minus two and two, the difference is eight.

And it's eight units, which I knew it would be anyway, because it's a square, but I've just wanted to check.

So then I knew that this one, there would have to be a difference of eight between the two x coordinates, because the y stays constant on a horizontal line.

And I knew there'd have to be a difference of eight in the y coordinates, because the x coordinate stay constant in a vertical line.

So therefore, I found my missing vertex, and I've got two different strategies to find it.

Now it's your turn, pause the video and use whichever strategy you prefer to find the missing vertex of the rectangle.

So as always, we annotate the known vertices.

So we've got.

And then we've got and , we see the vertical line, we see the same x coordinate.

So we know that this is going to be on a vertical line, it's going to have the same x coordinate, so it's going to be minus two, and it will be on a horizontal line with this vertex, so it will be minus four.

So it's at.

And we can check it.

So you may have used that strategy or you may use this other strategy where we look at the length of the shape.

So we're looking at the difference between the y coordinates here, the difference between one and minus four is five units.

And that's the same for the difference, in the I've written that one, and that's a four that's okay, we can see that in the difference between the one and the minus four there, you can see how important it is that we're really neat with our writing, because then you start to make mistakes.

And then we can look at the width of the shape, we're looking at the difference between minus two, and eight, which is 10.

So the width is 10 units, which you can see in the difference between the y coordinates here.

Now let's see another example.

This one is slightly trickier.

Now, here we have three vertices of a square, but the square is in a different orientation to the previous one.

So we're going to need to use some of our knowledge about squares to help us.

So as always, we start off with what we know, so we know that this is at And then we can see we're going to have a horizontal line here.

So they're going to have the same y coordinate, which will be four.

So it's two four.

And then this one is at and it's going to make a vertical line.

So it's going to have the same x coordinate, it's going to be minus one, but we need to figure out what the y coordinate will be according to the size of the shapes, okay? Now, we know that the black diagonals in a square are equal in length.

So if we look at the vertices on the horizontal line, we can see that they are six units apart so we can see the difference between minus four and two is six.

Okay, and therefore, we need to, we know that the missing vertex will be six units down the other way.

And it will make a vertical line.

So we know that we already said it will be at minus one, and we go six down from seven to one.

So the coordinates of the missing vertex are at because it's six units down that way as well.

So we have to apply our knowledge of shape to find the missing links in this one.

Now, I want you to pause the video and find the missing vertex of the parallelogram and use the annotations to guide your thinking.

So we can put on our known vertices minus four minus sorry, four minus eight to this one.

And then for this vertex, and 10, 11, 12, 13, minus four for this one.

So we are told that the width of the shape is six units.

So we know that across the top here as well, we are also going to have to have six units for our parallelogram.

So if we have a grid, that's really helpful, because we can just count six units.

But if we don't, we know our rules about horizontal lines, the horizontal line is going to have the same y coordinate, okay? It's going to be at something minus four, the x coordinate will be different, and it's going to be six units less than this x coordinate.

So 13 takeaway six is seven.

So the missing vertex is going to be at , which is here.

And we can count using the squares, one, two, three, four, five, six units.

And there we have our parallelogram that you can see.

Now it's time to put your learning into practise, pause the video and complete the independent task.

Click restart once you're finished, and we'll go through the questions together.

So question one, you had three vertices of a square plotted, but they were in the unusual orientation, so we had to do a bit of detective work.

So our known vertices are , which we can annotate on here, and all negatives because they're in the bottom left quadrant.

And you could see that the vertical line, they had the same x coordinates, we're going to have a horizontal line.

So we know that the y coordinate will be minus five, same as this one, but we need to figure out the x.

So we look at the diagonal, the diagonal length here in the square is four units.

So we know that it's going to be one, two, three, four across this way, this will be where our missing vertex goes.

And that will be at.

And we can see that the difference between the x coordinates on this horizontal line is four because the width of the shape the diagonal measurement was four units, and we have the same y coordinates because it is on a horizontal line.

In question two, you had three vertices of an isosceles trapezium.

And you needed to know the missing vertex coordinates.

We know how an isosceles trapezium looks like, it's going to look something like this.

So sometimes good to have a little sketch, we know that it's going to create a horizontal line with this vertex.

This one is at.

So we know that its y coordinate is going to be nine.

Now we need to look at the units here so we can see that it's two units this way.

So we're going to go two further that way and two up that way.

So we'll go two up here and it will end up here and we can see that that is at.

Eight on the x axis and nine on the y axis.

Simone has started to draw an equilateral triangle and she's plotted two vertices, you have to complete the triangle in two different ways.

So we can see that this is going to be three units high, and the vertex is going to go halfway between these two here.

So it's going to go up three units to here, or you may have gone down three units to here.

And there you have got a decimal coordinate.

So it went to minus.

And here, it went to the same x coordinate minus 3.

5, minus one So here you hook within the vertices of a rectangle, A and B were done for you, you have to plot D, which was at , so this is D, and you were asked to write the coordinates of C.

So this is a rectangle in a different orientation.

But you could see that the width of the rectangle was one square wide.

So you knew that it had to go here to C, one square away from B, and also two squares in length, and you've got that there as well.

So your missing coordinates for C, were.

And then your last one, three vertices were provided for a parallelogram.

So you have to plot these on your grid, , and and you needed to plot one more vertex.

So again, we're looking at the width of the shape here.

And we can see that it's four units because we have the grid to help us.

So we needed to just go four units that way.

Okay, and our missing coordinates were.

Great work, it's time for your final quiz so pause the video and complete the quiz.

Well done, you've worked really hard today.

That was not an easy lesson.

In our next one, we'll be solving more practical problems with coordinates and get ready to work really hard in our next lesson.

I'll see you then.