Lesson video

Hi there, my name is Miss Darwish.

And for today's math lesson, we are going to be describing the coordinates of a shape after it has been translated.

So before we start the lesson, if you could just make sure you are set in a nice, quiet, comfortable area ready to start.

So the agenda for today's lesson is first of all, We just going to recap on finding missing coordinates, then we're going to be having a look at some translations.

And then we're going to be looking at finding the missing coordinates after shape has been translated.

And then at the end of the session, as always, there will be a quiz for you to go and complete.

So before we start the lesson, if you can just make sure that you've got something like a piece of paper and a pencil, something to rub with and something to write on, and a ruler.

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

Okay.

Let's start the lesson.

So missing coordinates.

We can see our X axis and we can see our Y axis.

Now, we've got point marked in the third quadrant.

What do we know about that third quadrant? It has a negative X and it also has a negative Y.

Good.

So this point marked has, the coordinates minus five, three, minus five minus three, sorry.

So on the X, the X coordinate is minus five, and the Y coordinate is minus three, well done.

Okay.

So that's the minus five marked on the X and the minus three marked on the Y.

What I always do, especially with these missing coordinate challenging questions is whenever I get told the coordinates of any of the point, within a shape or just a point on its own, I always grab my pencil or my pen and I mark on the X axis and I mark on the Y axis straight away, okay, just so I can see what I know about the X axis on the Y axis.

So this point is one of four vertices of a rectangle.

And we know a rectangle will have four vertices.

So this is one of the coordinates.

Okay.

This point is one of four vertices of a rectangle.

Can you see what the other three points are? Now, can you guess what I'm going to tell you? I don't know the coordinates of the other three points.

So I want you just to have a think, see what maybe we already know.

And what we still don't know.

So I'm just going to have give you time to see what we already know and when we still don't know.

Okay.

Should we have a look together? So which other vertices do we know the coordinates of? So hopefully you had a think about that.

So the one in purple, do you know the X and Y of this? Do we know the X? Yeah, it has an X of minus five, we can see that on the X axis, it is minus five.

Do we know the Why? On that green line, there's nothing marked.

Okay? We don't know the Y.

We know the X, but we don't know the Y.

Well done if you said that.

Okay.

So it has an X of minus five, but we don't have enough information to know its Y coordinate.

Let's look at the next point then.

What do we know about this coordinate? Tell me what you know? Do you know the X? Do you know the Y? Do you know both? Okay.

We do know the X? We don't know the X.

If I went down on that X axis nothing is marked.

Do we know the Y? No.

Don't have enough information.

We don't really know the X or the Y just yet.

Okay.

And what about this one? We don't know the X on that pink line, nothing is marked there.

But we definitely know the Y coordinate, because it's minus three, is the same as the first one.

Well done.

Okay.

Let's have a look at another question.

So the coordinates of two vertices are written below.

So we have a quadrilateral shape, a rectangle to be more specific.

And of course, a rectangle has four vertices.

So we have, so all four vertices will have coordinates, obviously, and they're all in the first quadrant.

And that first quadrant, we know that X and Y are both positive.

So we don't quite know A and we don't know D, but we do know B.

What are the coordinates of B read them out to me? Five, two, well done.

And what's the coordinates of C? Eight, nine, well done.

So B is, five, two and C is eight, nine.

Okay.

We don't really have a question just yet, do we?.

The question hasn't been asked, but what was the first thing I said to you to do? To grab that pen or pencil and do what? Write down what we know.

We know the X and the Y for B.

We know the X and the Y for C and we can put these onto the X and the Y axis.

Okay.

Now, this shape has now been translated down 11 squares.

So this time is going to be a bit tricky.

So we still know B and C before they were translated.

Before the transformation of the shape.

What we do know about the shape is they've been moved down by 11 squares.

By how many squares? By 11 squares, well done.

Okay.

And these are the points.

So we've got A', B', C' and D'.

Now the question is, we want to know the coordinates for A' and D'.

So A' is the translated point for A, and D' is translated point for D.

It's going to give you some thinking time.

Okay Let's have a look together.

So, step one, let's solve this problem by using steps.

So step one is finding A and D.

So yes, we have to find A' and D'.

But before we even think about what happened to the shape when it was translated, let's go back and just find, let's look at the original shape before we did any transformations before we translated it down, and find A and D.

We were told B and C.

But we weren't told A and D, but we can find those out.

So, we know we're writing what we know remember that important step.

You grab your pen or your pencil and you write down what you know the X and the Y.

So B has a Y of two.

So I've marked that on there.

Can you see that? Okay.

And it has an X of five.

Can you see that? Okay.

So I've finished what writing what I know about B.

I guess what am going to do next.

I'm going to write what I know about D, well done C, sorry.

So B is five, two, we've done that one, and then I'm going to write what I know about C, eight, nine.

Y of nine, and an X of eight.

Now it's clear and now it's easy for me to see what the coordinates of the vertices A and D are.

Okay.

So let's just recap quickly.

If we translate a shape down, only the X or the Y coordinate change.

Some thinking time.

If we translate a shapes down.

What changes is that, the X coordinate that changes all the Y coordinate that changes and tell me in, five, four, three, two, one.

The Y coordinate that changes, well done because if we move up or down, it's the Y coordinate that changes because the Y is on the vertical line.

Okay.

So, we knew that B was five, two, we know that C is eight, nine.

Now that we've got everything else marked, what do we know now? So the first step was, what did we know from the question? We knew B and C the coordinates.

What do we now know after we've written everything out? I can see A, tell me the coordinates for A.

They're marked on there, five, nine, well done.

Tell me the coordinates for C again.

Eight, nine, well done.

Tell me the coordinates for B.

Five, two and tell me the coordinates for D.

Eight, two, well done.

See, everything is always super easy when we just grab that pencil or pen and we write down what we know from the question first of all, and then we start thinking, okay, what is the question now asking me to do? Now I can see.

Okay.

Now remember, we need to find out A dash and D dash.

So we know A and D.

We're feeling a bit more comfortable, we got to find A' and D'.

So, A' will be five something and D' will be eight something.

Why have I written the same X coordinates? Because our shape translated down so the X was staying the same, well done, the X was staying the same.

So it's safe for me to say, I know A has an X coordinate of five, and I know sorry, A' has an X coordinate of five same as A and I also know that D' has an X coordinate of eight the same as D.

What about Y? We go back to the question.

We, What did we do to the shape? We translated it up or down by 11 squares.

So we translated it down by 11 squares.

Okay.

And that meant that the Y coordinate was changing.

So, can you see the markings I knew the Y at B and D was two and A and C was nine and I need to decrease this by 11 because we're shifting it down by 11.

So, nine take away 11 is equal to minus two.

And then two take away 11 is equal to minus nine.

So now have we got our points the have we do we know that what the Y are for A' and D'? We do we've got minus two and minus nine.

Well done if you said that.

Okay.

Well done.

I know sometimes that can be a bit tricky but like I said, just writing everything down the information that we have makes it super, super easy.

Okay, now it's time for you to pause the video and have a go at completing the independent task.

Try your best, and then come back and we will check and go through those answers together.

Good luck.

Okay.

Welcome back, hopefully found that okay, should we go through the answers together now? Let's have a look.

So, this is the independent task that I left you with.

And it says this shape is translated 12 squares to the left, write down the coordinates of vertices B' and C'.

So what we've got in front of us is a grid with an X and Y.

And the quadrilateral is in the first quadrant, which tells us that everything in the first quadrant is positive.

So we've got points A, B, C, and D.

These are the four vertices, we know A, and we know D.

We don't know B, and C.

And actually, what we need to find is B' and C'.

So let's do this a step at a time.

What was that first step, tell me that we did? Or tell me the first step you did.

Okay.

Write down hopefully you said write down everything you know about the information given.

So put those markings on the grid.

Okay.

So, we then know that A has an X coordinate of three, and eight has a Y coordinate of seven.

D has an X coordinate of nine and D has a Y coordinate of three, well done.

Okay, so then we can see that B and C, B would have the coordinates three, three, and C would have the coordinates nine, seven.

Now, we are translating the shape to the left, if our shape moves, either right or left is the X or the Y going to stay the same or going to change.

what's going to change if we're moving left or right? In this case, we're moving left what's going to change, the X or the Y? The X is going to change as an X because the X is the horizontal line.

Okay.

So we should now have, if I go back, I've now got A', C' B' and D' and I can see that the Y the markings of the Y, okay, got seven and three and that hasn't changed because it's only the X that's changing.

Okay.

So A' will be minus nine, seven, B' will be minus nine, three.

C' will be minus three, seven, D' will be minus three, three.

Well done if you got those right if you've got a pen or a red pen to mark with then give it a big big tick if you got it right.

Just check through and hopefully as well you did your markings.

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 on Twitter, tagging @OakNational and to use the hashtag #LearnwithOak.

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

Now just wanted to say a massive bonus on all the learning that you have done today.

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

Good luck.