Lesson video

Hi, my name is Mr. Chan.

And in this lesson, we're going to learn about enlargement with a negative scale factor.

Here is an example.

We are going to enlarge shape A by a scale factor of -1 from point C.

So point C is our, what we call the centre of enlargement, and we're going to enlarge shape A using a scale factor of -1.

Now, it's easier to try and do these enlargements by seeing how far each vertex is away from the centre of enlargement.

So we're going to consider each corner of shape A one at a time.

We'll start with the bottom right-hand side.

So if we look at how far away the bottom right-hand side corner is from the centre of enlargement, we can see we've gone in the x-direction, -1 and in the y-direction, +1.

So we can write that as a translation vector.

1 in the x-direction and +1 in the y-direction.

So if we're enlarging by scale factor of -1, we multiply that translation vector by -1.

So that tells us where our corresponding corner is in our new enlarge shape.

So multiplying that translation vector by -1, we would get +1 and -1.

So that means from the centre of enlargement, we're going to go 1 in the x-direction, and -1 in the y-direction.

So that's basically 1 across, 1 down.

So we're going to do that with all the other corners.

So the top right-hand corner of shape A is -1 and +3.

So we have -1 in the x-direction and +3 in the y-direction.

Again, multiply that by the scale factor for the enlargement -1, we get a result of +1, -3.

So we're going to count those distances from the centre of enlargement.

So that's basically 1 across, 3 down.

And that's where our corresponding corner is in our enlarge shape.

Moving on to the next corner on the bottom left, that would be 4 to the left 1 up, so that's -4, +1.

Multiply that by the scale factor, and we get +4, -1.

So that's 4 in the x-direction, and -1 in the y-direction.

So that's where our third corner is going to be.

And for the very last corner, the translation vector is -4, +3.

Multiply that by -1, we get +4, -3.

So let's count that from the central enlargement, 4 in the x-direction, -3 in the y-direction.

We have now all our four corners to complete our enlarged shape.

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

So you can try this question by pausing the video and resume the video once you're finished.

Here are the answers.

What do you notice about the shape you start with, and where the enlarge shape ends up with these enlargements? What I noticed was that the original image that you start with and the enlarged shape are on opposite sides of the centre of enlargement.

Whereas, if we had positive scale factor enlargements, they are both on the same side of each other.

Now let's look at an example where we're enlarging shape A by a scale factor of -2 from the point of enlargement C.

So again, let's look at how far away our vertices are of shape A from the point of enlargement.

Again we're going to start with the bottom right-hand corner, that again would be -1, +1, so 1 left 1 up.

And if we multiply that by the scale factor, we can find where our enlarge shape for that corresponding point will be.

So we're going to multiply by -2, because that's the scale factor, we get a result of 2,-2, and that means 2 in the x-direction, 2 in the y-direction.

So that's 2 across, 2 down.

So 2 across, 2 down.

We get our corresponding point of the enlarge shape to be where the X is.

Now, let's look at the next corner.

So at the top right-hand corner for shape A, the translation vector for that is -1, +3, so that's 1 left 3 up, and multiply that by the scale factor, we get 2, -6.

So from the centre of enlargement, let's count that.

That's 2 across 6 down.

So our corresponding point will be there.

For the third corner, the bottom left corner for shape A would be -4, +1.

Multiply that by the scale factor, we get a result of 8, -2.

So let's count that across.

So our corresponding point will be there.

And the final corner for shape A will be -4, +3.

Multiply those distances by the scale factor of -2, we get a result of 8, -6.

So that's 8 across, 6 down and we can see the four corners of our enlarge shape.

We draw that in.

And notice with this enlargement it is a scale factor of -2.

So our side lengths were expecting to be twice as large.

So let's have a look.

So a base of 3 becomes a base of 6 and a width of 2 becomes a width of 4.

So all the side lengths have been doubled in size as we would expect.

Here's a question that you can try.

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

Here are the answers.

So when we have a scale factor of -2, I'm expecting the distance of the shape from the centre of enlargement to be twice as far away, but in the opposite direction.

But also, the each side length to the enlarged shape will be twice the size.

Can we see that happening? Let's have a look at this example.

We are going to enlarge shape A, which is a triangle this time by a scale factor of -1 from point C.

So let's look at our vertices in shape A, one at a time and count how far they are away from the centre of enlargement.

So the bottom right-hand corner is 1 of the left 1 up, which is -1, +1, 1 left 1 up.

Multiply that by the scale factor again, we get a result of +1, -1.

So that tells us that our enlarge shape, that corresponding corner has a point 1 across 1 down there.

So I've marked on the diagram.

Our second corner, we're going to look at the bottom left-hand corner for shape A, has a translation factor of -4, +1.

Multiply that by the scale factor, we get a result for the enlarged shape, the corresponding corner will be 4, -1, so that's 4 across, 1 down.

Let's mark that on the diagram.

Our third and final corner has a translation vector of -4, +3, we're going to multiply that by -1 and we get a result of 4, -3.

So let's mark that on the diagram.

And we can now draw in our enlarge shape.

So I can see that we've got a triangle, the scale factor is 1, so I'm not expecting the shape change size.

But what do you notice about that shape? I can see that it's been flipped upside down, and we call that inverted.

And that's something that you're going to find with enlargements of the negative scale factor.

The shapes will get inverted or flipped upside down.

Here's a question for you to try.

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

Here are the answers.

Now, it's not always going to be clear when you're enlarging squares or rectangles by negative scale factor enlargement, but you can see quite clearly when you're enlarging shapes like a triangle.

What happens to the shape when you enlarge it? Yes, you can see the shape gets inverted, or flipped upside down.

Here's another question for you to try.

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

Here's the answer.

Hopefully got this correct.

The scale factor for this enlargement is -1.

5.

So I'm expecting the shape to get inverted when I do the enlargement.

And secondly, the centre enlargement is 0,0.

That point on the coordinate grid is where the two axes intersect, also known as the origin.

That's all we have time for this lesson.

Thanks for watching.