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WJEC MATHEMATICS

INTERMEDIATE

GRAPHS

TRANSFORMATIONS

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Contents

Translation

Reflection

Enlargement

Rotation

Quick Guide

Translation – The shape is moved by a vector (𝑥𝑦)

Reflection – Flip the shape in a mirror line

Enlargement – The shape is made bigger or smaller by a scale

factor from a point

Rotation – The shape is turned a number of degrees, around a

point, either clockwise or anticlockwise

Credits

WJEC Question bank

http://www.wjec.co.uk/question-bank/question-search.html

PixiMaths Intervention booklet

https://www.piximaths.co.uk/intervention

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Translation

Another way of thinking about translation is ‘moving something

around’. The shape you translate will remain the same, but move left

or right and then up or down.

Example

Translate the following shape (shape A) four units to the left and 3

units down

The best way of answering this question is to choose a vertex

(corner) of the shape, move that point and then draw in the rest of

the shape.

A

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Vector notation

An easier way of saying ‘move 3 units to the right and 7 units up’ is

using a translation vector.

A translation vector takes the following form;

• The top number tells you how far right or left to move. If the

number is positive move right. If the number is negative move

left.

• The bottom number tells you how far to move up or down. If the

number is positive move the shape up. If the number is

negative move the shape down.

So, in the example above, you would need to move the shape 4

units to the right at 9 units down.

Exam Questions G3

1.

5

2. 3.

4. 5.

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Reflection

When reflecting a shape, we are given the line in which to reflect it.

There are some lines we need to know!

The line 𝑦 = 𝑥

𝑦 = ?

Sometimes the graph will be y=something (for example 𝑦 = 2)

To draw this, find 2 on the 𝑦 axis and draw a horizontal line

𝑥 = ?

Sometimes the graph will be x=something (for example 𝑥 = 2)

To draw this, find 2 on the 𝑥 axis and draw a vertical line

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To reflect shapes using a line of symmetry, draw a line (at a right

angle) from the shape to the line and use this same distance on the

other side of the mirror line.

Example 1

Here you can see each distance from

the mirror line is the same on both sides.

Example 2

This example shows the importance of drawing line at right angles

to the mirror line.

Exam Questions G4

1.

8

2.

3.

4.

5.

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Enlargement

To enlarge a shape, multiply every length of the shape by a scale

factor. (i.e. if the scale factor is 2, all sides will be twice as long and if

the scale factor is 1

2, each length will be half as long)

Examples

If you are not given a centre of enlargement you can draw the

enlarged shape anywhere. If you are given a centre of enlargement,

follow these steps;

• Draw a line from the centre of enlargement to one of the

shape’s vertices (corners)

• Multiply this length by the scale factor and, without moving your

ruler, draw a line of this length. This new point is the point from

where you should draw your shape bigger / smaller.

See an example over the page

Scale factor of 2 Scale factor of

1

2

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Example Enlarge the shape using a scale factor of 3, using A as the

centre of enlargement

A

Remember: Sometimes the scale factor is less than 1 (i.e. 1

2 ) so

your shape will be smaller.

Also, the centre of enlargement may be inside the shape. The steps

to your solution will be the same.

Example Enlarge the following using the point as the centre of

enlargement and using a scale factor of 2

The distance

from point A to

the top of the

triangle is 1.

Multiply this by

the scale factor

(3) means this

length needs to

become 3 units.

Once you have

found your new

start point, draw

the shape with

every length

multiplied by the

scale factor

The distance from

point to the vertex

above the point is 1.

Multiplying this by

the scale factor (2)

means this length

needs to become 2

units.

Once you have

found your new

start point, draw

the shape with

every length

multiplied by the

scale factor

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Exam Questions G5

1.

2.

12

3.

4.

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Rotation

USE TRACING PAPER FOR THIS

When rotating a shape, place your tracing paper over the shape and

draw around it. Then put your pencil point in the centre of rotation

(this is given in the question). Then rotate it as they ask for in the

question.

• 90 degrees is a quarter turn

• 180 degreed is a half turn

• 270 degrees is three quarters turn

[Know the difference between clockwise (the way the second hand

moves around a clock) and anti-clockwise (the opposite way)]

Example Rotate this shape 90 degrees anti clockwise about the

origin [Remember – the origin is (0,0)]

Step 1

Mark your point of rotation on the graph

Step 2

Place your tracing paper over the shape

Step 3

Place your pencil on the point of rotation

Step 4

Rotate using the direction and angle

given in the question

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Example 2 Rotate this shape 180 degrees anti clockwise about the

origin.

Exam Questions G6

1.

15

2.

3.

16

4.

5.

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Describing Transformations

For some questions you will be given the completed transformation

and you need to describe it. The following flow diagram (from

PixiMaths) is very helpful in deciding which transformation have you

been used.

• For an enlargement make sure you include the scale factor

and the centre of enlargement .

• For a translation make sure you include the translation vector.

• For a rotation include the centre of rotation, the angle, and the

direction (clockwise or anticlockwise).

• For a reflection include the equation of the mirror line.

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Exam Questions G7

Describe fully the

transformation that maps

Shape P to Shape Q

Describe fully the

transformation that maps

Shape A to Shape B

1.

2.

19

Describe fully the

transformation that maps

Shape A to Shape B

Describe fully the

transformation that maps

Shape C to Shape B

Describe fully the

transformation that maps

Shape A to Shape B

3.

4.

5.

20

Describe fully the

transformation that maps

Shape R to Shape Q

Describe fully the

transformation that maps

Shape A to Shape B

6.

7.