Lesson video

Hi, I'm Miss Davies and in this lesson we're going to be enlarging shapes by a positive scale factor on a coordinate grid.

Shape A has been enlarged to give shape B.

We've been asked to describe the enlargement.

When we're describing an enlargement, we need to state the scale factor and the centre of enlargement.

Let's start by working out the scale factor.

The width of shape A is two squares.

The width of shape B is four squares.

The width of shape A has been multiplied by two to give the width of shape B.

The height of shape A is one square.

The height of shape B is two squares.

The height of shape A has also been multiplied by two to give the height of shape B, therefore the scale factor is two.

To find the centre of enlargement, we need to draw lines onto our grid that connect the corresponding vertices.

These lines are called rays.

We could have also drawn rays onto the other corresponding vertices to confirm the centre.

These two rays intercepts at the point two, zero.

This means our centre of enlargement is two, zero.

Our full description of this enlargement is that it is by a scale factor of two from the centre two, zero.

Shape C is enlarged by a scale factor of three from a centre of three, negative one to give shape D.

We've been asked to draw shape D onto the grid.

Let's start by identifying our centre of enlargement.

This is the point three, negative one, which is here.

We're going to work with each vertex in turn.

Let's start with this bottom right vertex.

To go from our centre of enlargement to this vertex, we go up one square.

If we multiply this by our scale factor, we'll be going up three squares.

This is our coordinate for the enlarged vertex.

Next we'll look at this bottom left vertex to go from the centre of enlargement to this point, we go across two squares and up one square.

This is multiplied by the scale factor of three.

We need to go across six squares and up three squares.

Next, let's look at the top right vertex.

To go from our centre of enlargement to this point, we go up two squares.

This is multiplied by our scale factor of three, we're going to go up six squares.

Our final vertex is two across and two up from our centre of enlargement, so it's going to be six across and six up for the enlarged shape.

We can then join these vertices together.

We can check by drawing rays onto our diagram.

We can see that all of the rays intercept at the point three, negative one, meaning that this enlargement has been done correctly.

Here are some questions for you to try.

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

Here are the answers.

Shape K has been enlarged by a scale factor of two from centre zero, zero to give shape L.

The coordinates of shape N are eight, eight, eight, four, and 12, four.

This will give a right angle triangle.

Here are some questions for you to try.

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

Here are the answers.

In part b, vertex three, one is the centre of enlargement, which means that this vertex doesn't move, or we can say that it is invariant.

Here are some questions for you to try.

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

Here are the answers.

Make sure that you have stated both the scale factor and the centre of enlargement.

Here is a question for you to try.

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

Here are the answers.

Alex has used the centre of enlargement as one of the vertices of the enlarged shape.

That's all for this lesson.

Thanks for watching.