Lesson video

Hi, I'm Miss Davies.

In this lesson, we're going to be rotating objects around a given point.

In this lesson, we're going to be rotating objects around a given point.

Let's start off by rotating this rectangle about that bottom left vertex.

To start off with, we've rotated it a quarter turn or 90 degrees.

Now gone another 90 degrees, another 90 degrees, and then another 90 degrees to return it to the original starting point.

All of these turns were in a clockwise direction.

That means that they were turning the same way that a clock hand turns.

We could also have turned our rectangle in this direction.

We've gone 90 degrees, another 90 degrees.

So in total we've gone 180 degrees.

A further 90 degrees, 270 degrees in total, and then a final 90 degrees to return to our original position.

So that's 360 degrees in total in an anticlockwise direction.

So going the opposite way to the hands on a clock.

We don't have to rotate from vertex of the shape.

We can rotate around any point inside the shape or outside of the shape.

Let's see what happens when we rotate this rectangle about the point in the middle of the grid.

Let's rotate it 90 degrees anti-clockwise, another 90 degrees, 180 degrees in total, another 90 degrees or 270 degrees in total and another 90 degrees so 360 degrees in total back to where we started.

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.

If a shape has been rotated 180 degrees, it will appear to be upside down.

If this is the case, you don't need to state the direction.

As 180 degrees clockwise is the same as 180 degrees anticlockwise.

In this example, we've been asked to rotate the rectangle 90 degrees clockwise about it's bottom left vertex.

First thing we're going to do is place some tracing paper over our rectangle and draw the rectangle onto this tracing paper.

This is the Vertex that we are rotating the rectangle about.

We're going to put a pencil onto this point, then you can rotate the tracing paper 90 degrees clockwise and draw over the new rectangle.

This is our rotated shape.

We don't have to use tracing paper to do rotations.

Let's rotate this triangle 90 degrees anticlockwise about the point O.

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

Let's start with this one.

To go from this vertex to the centre of rotation, you have to go two squares to the left and one down, we're going to do the opposite of this.

We're going to go one square to the left onto these two lines form a right angle.

They are perpendicular to each other.

We can then mark this point.

Let's look at the next one.

We've gone four squares to the left and one down.

So we're going to go one square to the left and four squares up.

Again, these lines are perpendicular to each other.

Our final vertex, we go two squares left and four squares down.

Perpendicular to this would be four squares left and two squares up.

We can then join these points together to give our rotated image.

Which diagram shows the correct rotation of the rectangle 90 degrees clockwise about the point P? It is B.

We can say that all of the vertices have been rotated 90 degrees clockwise and that bottom right vertex has stayed in the same place as this is the centre of rotation.

Here are some questions for you to try.

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

Let's have a look at this first question.

This is the answer.

Our bottom left vertex to get to the centre of rotation, we go one square to the left and two squares down.

When it's rotated, it's two squares down and one square to the left again.

You can then repeat this with all of the other vertices to get this rotated image.

The second one is here.

What do you notice about these two diagrams? Well done if you realised that they're the same because rotating 180 degrees anticlockwise is the same as rotating 180 degrees clockwise.

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 question three, you could have rotated clockwise or anticlockwise it would give you the same result.

Here is a question for you to try.

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

Here is the answer.

Because this vertex doesn't move we can say it's an invariant point.

Because of this, it is the centre of rotation.

Here's 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 you've used the correct centre of rotation for each question.

That's all for this lesson.

Thanks for watching.