Lesson video

Hello, I'm Mrs. Lashly.

I'm looking forward to guiding you through your learning today.

Okay, so in today's lesson, we're going to translate objects from the information and that information might come in a variety of forms. So we're gonna be doing the doing of a translation during this lesson.

Used before and will be used during the lesson, translation, vector, congruent and vertices.

So there's two parts to the lesson.

The first part is thinking about just moving, translating a single point from descriptions.

And the second is to translate more complex objects.

So this lesson's all about translating things and we're gonna do it in two different parts.

So let's make a start on the first.

So to translate an object or a single point means you're gonna move it horizontally and/or vertically.

You don't always have to have horizontal and vertical, and it maintains its orientation.

So translation is a transformation that moves every point.

So if it's a single point, there's just one point, but if it's a shape, there might be many points, their vertices, by the same distance in the same direction.

And this maintains its orientation.

So here is an example of a translation, whereas this is not a translation.

So the second one is not a translation because its orientation has changed.

So if our description is to translate point A down by three and right by one, then that means translation is to move.

And we've now been told how to move it both vertically and horizontally.

So down by three would get you here.

So if you count one, two, three and then right by one, we'd end up here.

So this would be the image of A.

Sam says, "If we went right by one and then down by three, we get to the same point." Are they correct? So right by one, down by three, we get to the same point.

So Sam is correct.

It's important that actually, we should do the horizontal first.

So we should do what Sam suggested rather than the description.

So it's a good habit to do horizontal before the vertical in the same way as your coordinates.

So x before y.

x is a horizontal value and y is a vertical value.

Here we've got vectors.

So a vector is a succinct way of describing a translation.

It tells you about the horizontal displacement and the vertical displacement.

So translate point M by two, four.

So the two is the horizontal displacement.

Because it's a positive two, it's gonna go to the right.

And then four is the vertical displacement.

So that again is a positive four.

So it's gonna go up.

So this is where the image of M is.

So it's important, as I say, that you know that the horizontal is the top value because if the vector was the other way round, if four was the top value and two was the bottom, then our image would be in a different place because this vector means four to the right, two up.

So the same directions, right and up, but by different distances.

So the horizontal displacement, the vertical displacement are different.

Hence we end up in a different position.

If we've got a single coordinate on a coordinate axis, left by two and up by four, you can figure it out without using the coordinate axis.

So if it's moved left by two, then the x coordinate has gone down by two.

And if it's gone up by four, the y coordinate has increased by four.

So the 0.

32 would then be at one, six.

Two to the left, so the x coordinate is now on that line of x equals one, and then it's gone up by four.

So it's now on the six of the y-axis and that's where the image of A or three, two would be translated to.

So just to check from what we've just covered.

So two words that you need to figure out.

The bottom value in a column vector tells you the displacement, and if the horizontal displacement is negative, then you translate which direction? So hopefully, you've remembered or been reminded that the vertical displacement is the bottom value in a column vector.

And that's because it's the second place.

The same as the second number in a coordinate is the vertical.

So the horizontal displacement is your top number.

If it's negative, then you would be going to the left.

So have a look here.

We've got an image of a car and five shapes.

We've got a star, a trapezium, a circle, a triangle, and a pentagon.

The car translates by three, one, where does it finish? So which of those five shapes does it finish on? Hopefully you've said trapezium.

So three one, that vector means three to the right and one up.

Different vector this time.

So the car's translated by two, negative two, it's back where it started, two, negative two.

Which shape does it finish on? Hopefully, you said the circle.

So that time it went to the right by two and down by two.

Okay, so a check, the bicycle is translated by four, two.

Where is the image of the bicycle located? In that square of A or that square of B? So hopefully, you said B because it's moved right by four and then up by two.

So we're now onto the practise stage for yourself.

So question one, you've got four column vectors and you need to mark the image of L after each of those translations.

So for each one, you're starting at L again.

So I want the image of L four times.

When you're ready to move on, come back, but otherwise, pause the video and have a go.

So question two, you've got a grid with coins dropped all over it.

You're gonna start on the star, bottom left, and then you're gonna follow the trail of vectors.

So this time, you don't always go back to the star, you start from wherever you have ended up.

So you're gonna go two, two first from the star and then from that position, you're gonna go two negative one.

Now, as you go, if you land on money, then you collect the money and I want you to get the total.

Have a try.

When you're ready, come back.

And then question three is a bit more investigative.

So you have exactly the same money table and then all the money's back, even if you collected it last time and now you've got them same seven vectors.

I want you to investigate the total money you can collect if you changed up the trail order.

So could you find the lowest amount or could you find the highest amount? So you have to use all seven vectors.

You start from the star.

So have a little go at trying to find, can you get the biggest, can you get the smallest? Pause the video, and when you're ready, come back.

Okay, so question one, you needed to mark the image of L after each of those translations.

So I did say make sure you're always starting back on L.

So they are the positions that the images would be.

One, two means to the right by one, up by two.

Negative two, three means left by two, up by three.

Negative one, negative three means left by one, down by three.

And the last vector, three negative, two means three to the right and down by two.

So did you get the order correct? Horizontal, then vertical.

Question two, you needed to follow the trail.

Start on the star, follow the trail, and collect up any money that you land on.

So you should have got 1 pound 33 in total, and highlighted there are the spaces that you would've visited during the trail.

Question three was to investigate so that there's more answers than the ones on the screen.

But if you went A, two, two, then C, then F, then B, then G, then E, then D, that would've collected 3 pound 36.

So we must have landed on a two pound coin, I would imagine.

Whereas if you did E followed by A, followed by D, followed by F, followed by C, followed by G, followed by B, you'd have only collected five p.

So maybe you've got other ones.

Perhaps you got some of those as well.

Did you beat me? Okay, so we're back to the second part of the lesson.

And this is still translating, but this time, not just single points, some more complex objects.

So in your life, you will have translated more complex objects than points.

And this often happens on technology and dragging images.

So if you were on a slideshow software or a document software, then there's a chance that you've had to import an image and move it into a different place.

You didn't want it where the computer places it and you wanna drag it somewhere else.

And that is a translation because the whole image translates.

So here, this is where my image has ended up, but I might drag it into a different place.

Its orientation hasn't changed, it's not become mirrored, I haven't changed its size, it is congruent, it's just in a different place on my document.

And so that dragging nature is translation.

If you're just moving it horizontally and vertically, you are completing a translation.

And we can do this using tracing paper.

And there's a way of replicating that idea of moving the whole or translating the whole object.

So if you were to put tracing paper over your object, and this is quite a simple object, but it could be much more complex, it could be an image, a drawing as opposed to a polygon or a shape.

Here I'm just gonna mark the three vertices because it is a simple polygon.

I know that there's just lines between those.

So if we just mark those and then I want to translate, I want to see where my image would be after a translation, then I can move the whole tracing paper so that I can see where my image finishes.

So after the translation, where will the image be positioned? And so that's a way of replicating, just like you drag on a computer screen using your cursor, using your mouse and move it to a different position, tracing paper is a way of you showing yourself where it would be to end up.

But sometimes we don't always have tracing paper, so we might need a different way to do this.

And so we can do this by considering the vertices and translate them one by one.

So ignore the shape, but just think about them as single points.

So if we were to translate the point x in this case by the vector three, two, then the image of x would be x prime.

So I now know where that position is.

So if I now replicate that doing all the other vertices, there's only two more, it's a triangle, so if I do y, three to the right, two up, and then z, three to the right, two up, then my three vertices, the images of my three vertices are in the correct position because I did them point by point and I just then draw in the triangle.

So if you can identify points or vertices just doing them one by one, making sure they have translated by the same horizontal and displacement, the same vertical displacement will get you your image.

Alternatively, some of you may may have been thinking this as it was going through that last one, you could choose just to translate one of the vertices.

So just translate one vertex and then draw in the remaining part of the image.

Because you know a translation is, after a translation, the object and image are congruent, that means that the shape and the size and the angles will be the same.

So as long as you know its position by translating one point, you could then draw the shape in.

So here this triangle is, it's got a vertical height of two and a base of one.

So I can draw that in and label the other vertices.

So I only translated one single point and then I drew in the rest of the image.

So that's an alternative method.

Sometimes the complexity of the object may support one of those methods more than the other.

So for example, these two, so they're still polygons, they're still vertices linked with lines, but they're quite complex.

It's not just a right-angled triangle.

Which method do you think you would use for each of these? Maybe you would use a hybrid method.

Maybe you would translate a couple of the points, but draw the rest of it in because the left one, there's not many vertices, there's five.

So you could move them one by one.

It wouldn't take you too long, but it's getting more than three.

But drawing in, there's a chance that you could draw it incorrectly because of its complexity.

The second example has got many more vertices.

So plotting them one by one would take more time and therefore, perhaps you're thinking I'll draw that one in.

But that's where a hybrid method might come in that you decide to move to translate a few of those vertices, maybe three, four, five of them and draw the rest of it in.

So the more complex the image, you might need to start thinking about your methods.

So we're gonna translate this shape.

I'm gonna do this one, and then you've got one to do.

The object needs to be translated by the vector two minus three.

So two means two to the right, and minus three means three down.

So I need to translate this two to the right and three down.

If I start on A, seems sensible to start on A, that's where the image of A is.

B would be here.

And I might have done that by translating B itself, or I might have just looked at that B is one square below A.

So if B is one square below A, then the image of B is one square below the image of A.

Here's where C would be, and D, again, I could translate the vertex D, go two to the right and three down and that's where the image would be.

Otherwise, I might have thought, oh, it's three squares above C.

So my image of D is three squares above C.

Here's where E is, and F.

And then connecting them all up, I get my image.

So here's one for you to have a go.

So you are gonna translate the object by negative two, two.

So first of all, what does that vector mean? And then here's your object.

So where would the image lie? So you've got to move one vertex.

You've got to translate one vertex on either of the methods.

Either you're gonna translate each one or you're just gonna translate one and then draw the rest in.

But you need to translate one.

It makes sense to start with A.

So you should have gone left by two, up by two.

That's what that vector means.

Here's where B should be, the image of C and the image of D.

And so this should be your result.

After you have translated the object, this is where the image would lie.

Practise.

So the first task is about redesigning your layout of a bedroom.

So you've got drawers, you've got the bed, you've got a desk and a corner wardrobe.

So you are only allowed to translate those four objects within the room.

The curved arc is indicating where the door is.

So the door needs space to open in.

So you can't place anything within that arc area.

So there's a space there for you to draw.

Redesign your bedroom or this theoretical bedroom, making sure you are only translating.

Pause the video and come back when you're ready.

And then task two, you need to do six translations of this triangle.

So you're always gonna start with triangle A.

If you label inside the image, lowercase a, lowercase b, lowercase c so that you know which one relates to which vector.

So remind yourself what the vector means.

Horizontal displacement is the top number.

Vertical displacement is the bottom number.

And remember that you are always counting between corresponding points.

You can either move, translate each point, all three of them, or you could translate one and draw the other two in.

Pause video and come back when you're ready.

So question one, that redesign.

So this is just an example.

You may have got exactly the same as as this, but you may not have as well.

So there's a couple of things that you needed to be careful of.

So the drawers need to open.

So because it was a translation, the drawers would probably have needed to stay along that top wall.

If you had moved them to the bottom wall, then the drawers would now be against the wall and it loses function as a draw.

So it needed to stay along that top wall.

Potentially, I guess, you could have decided to have it away from a wall and then make like a little snug behind it.

But we tend to have them up against a wall.

So the drawer or the drawers would've been only been able to really translate horizontally.

The desk.

Well, this is where you may have made a decision on what this desk could be.

So the desk is the blue rectangle.

It was originally up against that wall.

And if that's a desk that also has drawers or a pullout keyboard shelf or something, then it would need to stay along that wall.

If it's a desk, like a tabletop desk that's not got any drawers underneath it, or as I say, any sort of pullout, it might be that it doesn't matter which side goes up against the wall, it's still a functional desk.

So that blue one may be against the left wall, it may be against the right wall without translate.

So with translating it, you could move it up and down and you can move it left and right.

It depends on what type of desk you decided that was.

Again, with the bed, I've decided that this bed has got sort of it's symmetrical ends, that there's not sort of a headboard as such.

So I've just moved it onto a different wall.

And making the decision that your bed cover and quilt and pillows can move either side of the bed and that's not a problem.

So just focusing on the furniture, it could be there.

Then lastly though, the pink corner wardrobe had to stay there if it is to remain touching two walls.

So because we could only translate, so move it left and move it right, move it up, move it down, it had to stay in that position if you were to have it remaining to touch two walls.

If you decided that you're not gonna have it touching two walls, then yes, it could be right in the middle of the bedroom.

Wouldn't be very sensible, I don't think, but it could be.

But if you were remaining at touching at two walls, then that is the only position it could continue to be on.

Okay, and then question two, six translations needed to take place.

What may have happened here if you've got them in the wrong places, you just go back to those vectors.

Did you do horizontal before vertical? And remembering, negative means left or down and positive means right or up.

So during this lesson, we've looked at translating objects.

So you can choose one vertex of the object and translate that before drawing in the rest.

You could translate every vertex of an object to form the image, and that image will always be congruent after a translation.

Well done today and I look forward to working with you again in the future.