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Welcome to our fifth lesson in this topic, coordinates and shapes.

Today, we'll be solving problems involving coordinates.

All you'll need is a pencil and a piece of paper.

These are our agenda.

So we'll be solving problems involving coordinates, starting with a quiz to test your knowledge from the previous lesson, then we'll find missing coordinates and simple shapes before moving onto more complex shapes.

Then you'll complete some independent work before doing the final quiz.

So we're starting off straight away looking at missing coordinates and shapes.

So here we have three vertices of a square and they're plotted at the points indicated.

We have to find the coordinates of the missing vertex.

So if you think back to our learning in the previous lesson, and we're thinking about horizontal and vertical lines.

So the bottom two vertices are on a horizontal line, which means that the Y coordinates are the same.

So there Y coordinates are both minus six because they're at the same point on the Y axis.

And then the difference between the X coordinates tells us the length of the shape.

So we can see that we've got minus seven and minus one.

And the difference here is six.

So the shape is six units wide.

And remember it's a square.

So we know that it's also going to be six units in length as well.

So we can also see this confirmed when we look at the vertical line.

We can see that the X coordinates are the same, because the points are at the same position on the X axis.

But the Y coordinates are different and they have a difference of six units.

Zero and minus six, the difference is six units.

So now we can work out the missing coordinate by using the information that we have worked out.

So we know that it's going to have the same Y coordinate because it's on a horizontal line.

So the Y coordinate will be zero.

And the X coordinate will be six less than this one, minus seven, subtract six, sorry, six more because we're going towards zero.

So minus seven plus six is minus one.

And then we can check it with other known knowledge.

We've got another vertical line here, and we can see that the X coordinates are the same because on a vertical line, the X coordinates are all the same.

So we've used both of our strategies there.

When to do it and when to check.

So now we've got the three vertices of a rectangle and we have to find the coordinates of the missing vertex.

So we can use our two strategies.

Okay.

First one is that these two are on a horizontal line.

So we know they'll have the same Y coordinates.

So we know that the Y coordinate will be minus four and they're on these two are on a vertical line.

So they will have the same X coordinate, which is minus one.

Let's check it using our strategy to see the length of the shape.

So we can look at the length of the shape by looking at the Y coordinates here.

So we're looking for the difference between six and minus four, which is 10 units.

And then we can see that difference with these Y coordinates.

And then the width of the shape is the difference between minus one and three, which is four units.

And unlike our previous lesson, in today's lesson, we don't have any squares on our coordinate grid.

Therefore, we need to rely on the strategies that we learnt.

Which is that when we have a horizontal line, the Y coordinates are the same.

When we have a vertical line, the X coordinates are the same, and you can use this to find out the width and the length of the shape.

Let's look at another one together.

We've got three vertices of the square plotted at the points indicated, but the square is in a different orientation to what we've seen previously.

We need to use our knowledge of squares here, and we know that the missing vertex is going to be inline in a vertical line with this one, so we need to use the line here for the length of the diagonal of the square, so that we can find out where this one should be plotted.

So these two are on a horizontal line, so they have the same Y coordinates, and we use the X coordinates to find the width of the diagonal.

So the difference between minus four and zero is four units.

So we have to go that way down four units as well.

These two we've already said are going to be vertically in line, which means that they will have the same X coordinate of minus two, but the Y coordinate will be four less than this one, seven subtract four is three.

So the missing vertex is a minus two three.

Now pause the video and find the missing vertex.

Three vertices of a rectangle are plotted at the point indicated.

What are the coordinates of the missing vertex? So you could either have looked at these vertical and horizontal lines.

So with the vertical line, you are given the X coordinate of minus three, and the horizontal line you're given the Y coordinate of minus four, or you could have looked at the difference between the X coordinates and seeing that it was three units wide.

And the difference between the Y coordinates, it tells us that it is six units in length.

But it's important that you've got the two strategies to get into which one works best for you.

Now let's go on to some more complex shapes.

So here we've got two rectangles put together on our coordinate grid, and we need to find the coordinates of point A and point B.

And we need to use the known coordinates to find the length and width of the shape.

So we'll start with the width.

We're looking here at the X coordinates.

The difference between six and 10 is four units.

So we know that both rectangles are four units in width.

Now, when we're looking at the length, we need to look at the whole rectangle at one point.

So we can see that looking at the Y coordinates here, we've got 14 and two, and the difference there is 12 units.

So both rectangles together are 12 units in length.

So each one is half of that.

So they're six units.

Okay.

So now we know the measurements of the rectangles.

We'll start to work out the missing coordinates.

So we'll use this one to help us, okay.

This is in a vertical line with the one that is known.

So we already know that the X coordinate is 10 because it stays the same in a vertical line.

Now we look at the Y coordinate and this one is two, but in A it's six units higher up.

So we add two and six, and that gets us to eight.

Okay.

And then we can also check that, because we can see the difference between eight and this Y coordinate 14 is also six.

And we look at B, we can again use this one to help us.

So these are on a horizontal line.

So we already know that the Y coordinate is going to be two.

And then we know that the X coordinate is going to be four more than this one.

And 10 plus four is 14.

So B is at 14 too.

Now here's another one.

I want you to have a go at this one by yourself.

So the diagram shows two identical squares, and you are given some of the coordinates and you need to figure out, what are the coordinates of A and B.

Pause the video and have a ago by yourself.

So I know that the sides on the square are the same length, so I just need to figure out one of the lengths.

Okay.

So I'm going to look here at the difference between the X coordinates four and 14.

So the differences 10.

So all of the sides are therefore going to be 10 units.

I'll just put this on here because I personally find it really helpful to annotate my diagrams. Okay.

So now I'll use my known to figure out A.

So A is on a horizontal line with this known.

Therefore we know that our Y coordinate will be the same, and then the X coordinate, because it's 10 units wide is going to be 10 greater than this one and four plus 10 is 14.

So A is 14 zero.

B is on a vertical line with the known one.

So we know that the X coordinate is four.

And then it's going to be 10 more than the Y coordinate and zero plus 10 is 10.

So that one was at four 10.

Now it's time for you to do some independent learning.

Pause the video to complete the task and then press restart once you're finished so that we can go through the answers together.

So in question one, you had a partially completed diagram of an isosceles trapezium.

So, as I said in the previous lesson, sometimes it's helpful just to have a little sketch of what you're the sort of thing that you're going for.

Okay.

So as you can see, I've already annotated on here.

I can see that the height of the shape is 14 units, because I looked at the difference between the Y coordinates 18 and four.

And I can also see that that distance between the inside points and the outside points is four units because of the difference between the X coordinates 20 and 24.

So I need to subtract four units from the X coordinate to get the X coordinate, the missing point.

I can sketch it on there.

I know it's going to be roughly here.

So therefore I know that the X coordinate is going to be four less than 14, which is 10 and the Y coordinate it's on a horizontal line with this one at the bottom.

So the Y coordinate will be four.

Question two.

You had a pattern made of three congruent squares, which means identical.

And you had to find the coordinates of points, M and J.

So the width of the three sketch squares is 21 units.

That's because of the difference between the X coordinates 24 take away three is 21.

So therefore I knew that if three were 21, then each one is seven, 21 divided by three is seven units.

And I know that the lengths are the same as the width in a square.

So I could put that annotation on as well.

So each side is seven units.

So for M, I look at the one above three 23, I know it's on a vertical line.

So the X coordinate will stay the same.

So it will be three.

And then the Y coordinate will be seven less.

So 23 subtract seven is 16 because the height of the square was seven units.

So then I can look at J I can use this one 24 23, the X coordinate will be seven less than 24.

So it will be 17.

And then the Y coordinate will be 14 less than 23, because it's seven and seven there.

So that is nine.

So J is 17 nine.

For question three, we had a reflection of an equilateral triangle.

Unlike in our previous lesson, the mirror line was not one of the axes, but it's the same principle.

The vertices are the same distance from the given mirror line.

And you are asked to find the coordinates of the missing vertices.

So I can see that each side is eight units by looking at the difference between the X coordinates.

And then I can see that I'm going to add eight to the X coordinate here, which will be 28.

And the Y coordinate is a constant on a horizontal line.

So that's going to stay as four.

The height of the triangle is also eight units.

So I'm going to add eight to the Y coordinate.

So the Y coordinate will be 12.

Okay.

Eight more than four.

And then I know that the X coordinate is going to be halfway between 20 and 28.

And that is 24.

So our unknown at the top is 24 12.

For question four, you were given three vertices of a parallelogram.

So a sketch of what we're sort of looking for roughly.

So we know that it's going to be somewhere probably around here.

So then we're going to find the missing vertex.

So we can see that the difference here between the outside and the inside points is four units.

And that's all that we need here.

So we know we're subtracting four units from the X coordinate, which is 23.

And we know the Y coordinate is going to stay constant because it's on a horizontal line with this one.

So it will be 23 19.

And then finally question five, you had a rectangle drawn on the axes and the diagonals were drawn in, and you had to find the coordinates of P and K.

So I've annotated already.

The width of the rectangle is 21 units.

So half way is where K is.

So that's 10.

5.

So we know that the X coordinate is 10.

5.

And we know that the height of the triangle is eight.

Okay.

And then half way up is four.

So we're going to add four to our Y coordinate seven which is going to be 11.

So K is 10.

5 11.

Let's get my brackets.

And then P we can see that P is on a vertical line with this one.

So we already know that the X coordinate stays the same, and then the Y coordinate will be the seven plus eight, which is 15.

So P is 21 15.

Looking great.

Okay.

It's time for your final quiz.

So pause the video and complete the final quiz and click restart once you're finished.

Great work today.

In our next lesson, we'll be learning to recognise 3D shapes and their nets.

I'll see you then.