 # Use Rotation

In this worksheet, students practise rotating an object. Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Geometry and Measures, Congruence and Similarity

Curriculum subtopic:   Properties and Constructions, Plane Vector Geometry

Difficulty level:   ### QUESTION 1 of 10

What is rotation?

Rotation in Maths is where you take a shape and turn it.

What do I need to rotate an object.

If you tried to describe something that was turning in real life, you would need to give three pieces of information.

Which way it was turning, how far it turned and what it was turning around.

In Maths, these would be called...

1) Distance - How many degrees the object was turned. At GCSE maths, this is normally limited to 90°,180° and 270°,

2) Direction - This is referred to in Maths by clockwise (CW) and anticlockwise (ACW)

3) The Centre of Rotation - In any rotation, there is a point that doesn't move. We define this point as a coordinate.

How to rotate an object.

There are a couple of pieces of equipment you need here. Firstly a pencil (sharpened) and secondly some tracing paper (Greaseproof kitchen paper works just as well)

Example 1: Rotate this triangle 90° clockwise around the point (1,1)

Step 1: Draw out what information you are given.

Sometimes, the shape will be drawn for you, but if not, draw the shape AND the centre of rotation. Step 2: Trace.

Put your tracing paper over your shape, making sure you cover the centre of rotation.

I would recommend that when you trace the centre, draw a cross over the centre, this makes it easy to see if you have rotated exactly 90°. Step 3: Complete the rotation.

Place the point of your pencil on the centre of rotation (this makes sure it doesn't move while you turn the tracing paper) and turn the tracing paper 90° clockwise. Step 4: Transfer the image and label.

The easiest way to transfer the shape back onto the paper is to press on the corners of the shape with your pencil (do this lightly)

This will give three little dips in the paper underneath that you can just join up to finish the shape.

Remember that if the image is labeled a, the rotation will be labeled a' When we are rotating an object, we normally need three pieces of information...

Rotation 180° does not need a direction because it will end up in the...

Rotating 90° clockwise is the same as...

This shape has been rotated anticlockwise. How far has it been rotated? (Don't put in the degree sign, just concentrate on getting the number correct)

Which of the transformations could describe this transformation? 90° CW

90° ACW

180°

270° CW

270° ACW

Is this a clockwise or an anticlockwise rotation? Clockwise

Anticlockwise

We can't tell

I rotate this shape 90&deg; clockwise around the origin.

What are the co-ordinates of b'? HIN: Try drawing it out first.

Clockwise

Anticlockwise

We can't tell

I rotate this shape 180° around the origin.

What are the co-ordinates of b'? HIN: Try drawing it out first.

Clockwise

Anticlockwise

We can't tell

I rotate shape a 180&deg; around the point (2,1)

Which of the two rotations is correct? Shape 1

Shape 2

I rotate shape a 180° around the point (1,-1)

Which of the two rotations is correct? Shape 1

Shape 2

• Question 1

When we are rotating an object, we normally need three pieces of information...

EDDIE SAYS
You need to remember these three. When you come to describing a rotation, you need to give all three to get full marks.
• Question 2

Rotation 180° does not need a direction because it will end up in the...

EDDIE SAYS
Try it. Take something (a book, a pen etc), turn it 180 clockwise and then 180 anticlockwise. It'll end up in the same position.
• Question 3

Rotating 90° clockwise is the same as...

EDDIE SAYS
turning 1/4 turn one way is exactly the same as turning 3/4 of a turn the other way. Try it if you don't believe me.
• Question 4

This shape has been rotated anticlockwise. How far has it been rotated? (Don't put in the degree sign, just concentrate on getting the number correct)

270
EDDIE SAYS
If we are going anticlockwise, the shape has been turned 3/4 of a full turn. How many degrees is this the same as?
• Question 5

Which of the transformations could describe this transformation? 90° CW
270° ACW
EDDIE SAYS
Whenever you do a rotation, there is always two ways to describe this. For this one, I could have done 1/4 clockwise or 3/4 anticlockwise
• Question 6

Is this a clockwise or an anticlockwise rotation? We can't tell
EDDIE SAYS
As I mentioned last time, there are always two ways you could have done the rotation. Without more information, we can't say which way it has turned.
• Question 7

I rotate this shape 90&deg; clockwise around the origin.

What are the co-ordinates of b'? HIN: Try drawing it out first.

EDDIE SAYS
A couple of things to remember here. 1) The origin is the point (0,0) 2) b\' is the rotated version of point b
• Question 8

I rotate this shape 180° around the origin.

What are the co-ordinates of b'? HIN: Try drawing it out first.

EDDIE SAYS
A couple of things to remember here. 1) The origin is the point (0,0) 2) b' is the rotated version of point b
• Question 9

I rotate shape a 180&deg; around the point (2,1)

Which of the two rotations is correct? Shape 2
EDDIE SAYS
The easiest way to do this is to draw it out and do it yourself. The mistake people often make here is to rotate around the origin instead of the point that is given. (this is where shape 1 has come from)
• Question 10

I rotate shape a 180° around the point (1,-1)

Which of the two rotations is correct? Shape 1
EDDIE SAYS
The easiest way to do this is to draw it out and do it yourself. Be very careful when plotting your centre. Shape 1 has been rotated about (1,-1) and shape 2 has been rotated around (-1,1). Can you see how much of a difference plotting your coordinates the wrong way round can make?
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