Lesson video

Hi, my name is Miss Kidd-Rossiter, and I'm a maths teacher from Hull.

I'm really excited to take you through today's lesson, on enlargements from a given point.

Part of this really great unit on enlargements.

Before we get started, please make sure that you've got no distractions and that if you're able you're in a nice quiet place, so you can concentrate.

If you need to pause the video now to get everything ready, if not, let's get going.

So we're going to start today's lesson with the, Try this, pause the video now, read the activity and then give this task your best go.

When you're ready to discuss it, resume the video.

So the first thing you were asked to do was to find the scale factor of enlargement from ABCD to EFGH, we can see the ABCD has a width of one square, and height two squares and EFGH has a width of two squares, and a height of four squares.

Therefore, we can quite clearly say that the scale factor of enlargement is two.

Then we were asked to look at what do we notice about the lengths? OA, and OE.

You should have noticed, that OA, is half of the length of OE.

Or you could have said that, OE is double the length of OA.

How does that relate to our scale factor? Then you were asked to look at OD to, OH.

What do you notice here? OD is half of the length of OH, Or, OH, is double the length of OD.

Again, how does this relate to our scale factor? And lastly, we were asked to look at OB and BF.

These two are the same length.

Why might this be? Let's look at this a little bit further in the connect activity.

So you've got two pictures on your screen, which show an enlargement, a scale factor three, You've got two different methods there.

I want you to pause the video, read the methods and think about which method you would recommend and why.

Well, I'm thinking about that.

Both of these are really valid methods, but we might use them at different times.

So the method on the right hand side, this method here, we would use if we were not enlarging from a given point, cause we're just comparing the size of the object, and the size of the image.

When we're asked to enlarge from a given point, this is the method we might choose to use.

I'm going to show you why now.

So I'm going to show you now about how we use these ray lines, which is the name of these dotted lines here, we should use to find enlargements.

So you can see that I'm going to enlarge this shape here by a scale factor of three.

So I'm going to show you what that looks like now.

And that enlargement is from this given point.

If I move this point, you'll see that the position, of my image moves.

So I can move it closer to my object, or I can move it further away.

I can also move it on an angle either that way, I can move anywhere.

But when I moved the centre of enlargement, the position of my image moves.

You'll notice that the size of the image doesn't change because it's still being enlarged by a scale factor of three.

So if we look at this here, we can see that, from the centre to this Vertex, it's one diagonal square.

If we repeat to this corresponding Vertex on the image, we can see it.

It's one, two, three diagonal squares.

So the distance from the centre of enlargement to the Vertex has also increased by the same scale factor, it's gone from one to three.

The key points to note from this section are that the centre of enlargement changes the position, of the image.

It does not change, the size.

So it's your turn now to have a go at applying what you've learned, pause the video, navigate to the worksheet, and then check back in for the answers to the independent task.

Good luck! Okay, so let's go through some of the answers to this independent task then.

So first of all, you had to enlarge the shape by scale factor two with a centre of one, two.

So you can see on the diagram that I've already plotted the centre, one, two the next thing I would do is I would draw my ray lines in and measure from my centre, to each of the vertices and then enlarge this by scale factor two.

This then gives you the new shape, which should look like this.

Question two, you again had to use scale factor two centre zero, zero.

So first of all, I've plotted my centre zero zero.

And then I've drawn my ray lines in which aren't going to appear on the screen, but you should have done that.

And my new shape enlarged by scale factor two should look like this.

We've got the same centre, for part B, but it's a scale factor of 0.

5, which we know makes this shape smaller.

So you can see on the diagram, what that should look like.

And finally, our scale factor two centre one two, means our center's going to move to here.

And therefore our enlargement should look like this.

This was a tricky question so well done if you did this.

I would do it by drawing ray lines in, to see whether the centres are in the correct place.

So first of all, on A, my rail lines look like this, which show me that my centre should be here.

So for A, the centre is in the wrong place.

For B, my rail lines look like this.

And this time I can see where the rail lines meet.

Is it B? So my centre is in the correct place this time.

And for C I can see that my rail lines meet here.

So this means that my centre is in the wrong place for C.

Right, so we're moving onto the explore task now, which is on your screen.

You're going to need a pen and paper, and you're going to need to play with this for quite a while.

Good luck, and tune back into the video, once you've had a good go.

Excellent work today.

I hope you've had a really good go at trying this task.

There's so much in this, and I'm sure that you could keep going with it for hours, if you really wanted to.

I hope you've learned loads today.

I've had a really good time teaching you, and I hope to see you again in the future, bye!.