Lesson video

Hi, my name is Mr Chan, and in this lesson, we're going to learn how to describe an enlargement with a negative scale factor.

In order to describe an enlargement with a negative scale factor, we've got to know two piece of information.

And the first piece of information we need is finding where the centre enlargement is.

So we're going to look at this example where we're going to identify where the central enlargement is from shape A to shape B.

How we do that is find corresponding corners for both shapes.

So it's a little bit more tricky with a negative scale factor enlargement because the shape has been inverted from the original.

So the enlarged shape is flipped upside down.

But with a bit of practise, you'll find this pretty straightforward.

Now I'm going to look at my bottom right hand corner of shape A and I'm going to draw a line to the corresponding corner of shape B.

Now, as I've said, a negative scale factor enlargement the shape's been flipped upside down.

So the corresponding corner for the bottom right corner of A will be the top left of B.

So I'm going to draw a line joining those two corners up.

And for every other corner I'm going to do exactly the same thing.

So the bottom left corner of shape A the bottom of that vertex will be joined up with the top right vertex of shape B, and I'm drawing a line.

And the next is the top left corner of shape A, will be joined up with the bottom right corner of shape B and similarly the top right corner of shape A will be joined with the bottom left corner of shape B.

Now those four lines that I've drawn, you'll notice one thing that they all converge at one point.

And that point is where the central enlargement will be.

I hope you've managed to get hold of the worksheet for this lesson.

It'll make answering these questions a lot easier.

So pause the video to have a go, resume the video once you're finished.

Here are the answers.

Hopefully your answers match up with the answers given here.

However, be really careful and precise when you're drawing your lines joining corresponding points, because it's quite easy to make a little mistake.

So let's recap how we identify the centre of enlargement of shape A to shape B.

We find corresponding corners of both shapes, and we draw a straight line joining them together.

So once we've drawn those lines joining those corresponding corners together, they will converge at one point.

And that's where we call our centre of enlargement point.

So we can see that on the diagram there.

Now that's the first piece information we need in order to describe an enlargement.

The next piece of information we need is identifying what the scale factor is.

And how we do that is find corresponding side lengths.

So we look at the side lengths of A that we can easily count.

So let's look at the base of A.

We can see that that's three squares in length.

We look at the corresponding side length of B, That would be six.

So what we can say there is we can see that that's doubled, but we also just double check, by looking at the other corresponding side lengths.

So the height of triangle A is two squares high, and the corresponding length in B is indeed four.

So what we can see is it's a scale factor of two.

However, let's not forget that the shape B has been inverted, it's been flipped upside down.

So that indicates a negative scale factor.

So what we say about the scale factor enlargement of shape A to B it is negative two.

Here's a question that you can try.

Pause the video to complete the task, resume the video once you're finished.

Here's the answer.

Hopefully you managed to put negative two as your scale factor for this enlargement.

We know is negative because the shape has been flipped upside down or what we call inverted.

So now let's try and put everything together that we've covered so far.

In this example, we are going to describe fully the single transformation that maps shape A onto shape B.

So what we do first is try and identify where the centre of enlargement is.

So we do that by finding corresponding vertices and join them up with a straight line.

So each corresponding corner, we join them with a straight line and we will find that they converge at one point and we can see where that point is on the diagram.

That's the coordinate one zero.

So my centre of enlargement, we can write down as 1, 0 as a coordinate point.

Now our next task is to identify the scale factor.

So we find the corresponding side lengths.

So I'm looking at the side of shape A as two squares in length and in shape B is one square in length now, a mistake would be here to say that the scale factor is two, but be careful because it does say shape A to shape B.

So from shape A to get to shape B, the shape is actually getting smaller.

So it's a fractional scale factor here.

And that works with the side lengths as well two to one.

So what's actually happening here is, the scale factor is negative 0.

5.

We're multiplying by a half and we know it's negative because shape B is getting inverted.

It's flipped upside down.

So putting all that together to try and answer this question, we would say the shape A has been enlarged by a scale factor of negative 0.

5, where the centre is one zero to give shape B.

Here's a question for you to try, pause the video to complete the task, resume the video once you're finished.

Here's the answer.

Hopefully you got those two pieces of information correct, the scale factor and where the sense of enlargement is.

However, this question also asks what transformation is.

So you must also tell whoever's asking the question that it is actually an enlargement.

Here's another question for you to try.

Pause the video to complete the task, resume the video once you finished.

Here's the answer.

I hope you read the question really carefully, because it tells you that shape A maps to shape B.

And you can see shape B is smaller.

So that means you're expecting a scale factor for the enlargement of a number between zero and one or even a fraction.

And in this case, the scale factor is negative 0.

5.

That's all we have time for this lesson.

Thanks for watching.