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
A
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.
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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.
4
2.
4.
3.
5.
5
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.
7
2.
3.
4.
5.
8
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
1
the scale factor is 2, each length will be half as long)
Examples
Scale factor of 2
1
Scale factor of 2
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
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Example Enlarge the shape using a scale factor of 3, using A as the
centre of enlargement
A
The distance
from point A to
the top of the
triangle is 1.
Multiply this by
the scale factor
Once you have
found your new
start point, draw
the shape with
every length
multiplied by the
scale factor
(3) means this
length needs to
become 3 units.
1
Remember: Sometimes the scale factor is less than 1 (i.e. 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
Once you have
point to the vertex
found your new
above the point is 1.
start point, draw
Multiplying this by
the shape with
the scale factor (2)
every length
means this length
multiplied by the
needs to become 2
scale factor
units.
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Exam Questions G5
1.
2.
11
3.
4.
12
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 3
Place your pencil on the point of rotation
Step 2
Place your tracing paper over the shape
Step 4
Rotate using the direction and angle
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given in the question
Example 2 Rotate this shape 180 degrees anti clockwise about the
origin.
Exam Questions G6
1.
14
2.
3.
15
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
1.
Describe fully the
transformation that maps
Shape P to Shape Q
2.
Describe fully the
transformation that maps
Shape A to Shape B
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3.
Describe fully the
transformation that maps
Shape A to Shape B
4.
Describe fully the
transformation that maps
Shape C to Shape B
5.
Describe fully the
transformation that maps
Shape A to Shape B
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6.
Describe fully the
transformation that maps
Shape R to Shape Q
7.
Describe fully the
transformation that maps
Shape A to Shape B
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