Define the term translation .

A translation is when a shape is moved . Its position changes but its size, shape and orientation stay the same.

How do you translate a shape?

Move each corner according to the vector. Join the new corners together to make the translated shape.

True or False? When you translate a shape, it should not overlap with the original shape.

False. When you translate a shape, it can overlap with the original shape.

To get full marks, what information do you need to give when describing a translation in an exam question?

When describing a translation , you need to: state that the transformation is a translation state the vector

Define the term reflection .

A reflection is when a shape is flipped about a line of symmetry. Its orientation changes and its position could change but its size stays the same.

Which points do not change when reflected?

The points on the line of reflection do not change when reflected.

How do you reflect a shape about a line of reflection?

To reflect a shape, reflect each corner separately. Count or measure the perpendicular distance from a corner to the line of reflection Repeat this distance on the other side of the line Label the new corner Join all the corners up to form the reflected shape

To get full marks, what information do you need to give when describing a reflection in an exam question?

When describing a reflection , you need to: state that the transformation is a reflection state the equation of the line of reflection

Define the term rotation .

A rotation is when a shape is turned about a point. Its position could change but its size stays the same.

True or False? A rotation 90 ° clockwise is the same as a rotation 270 ° anticlockwise .

True. A rotation 90 ° clockwise is the same as a rotation 270 ° anticlockwise .

True or False? You must state the direction of the rotation when the angle is 180° .

False. You do not need to state the direction of the rotation when the angle is 180° . 180° clockwise is the same as 180° anticlockwise.

To get full marks, what information do you need to give when describing a rotation in an exam question?

When describing a rotation , you need to: state that the transformation is a rotation state the angle and direction of the rotation state the position of the centre of the rotation

How do you rotate a shape about a centre of rotation?

To rotate a shape: Trace over the original shape Put your pencil on the centre of rotation Rotate the tracing paper by the given angle and in the given direction Draw the rotated shape as indicated by the tracing paper

True or False? The centre of rotation can be inside the original shape.

True. The centre of rotation can be inside the original shape.

Define the term enlargement .

An enlargement is when a shape is stretched (or shrunk) both horizontally and vertically by the same factor.

True or False? Enlargements always make shapes bigger .

False. Enlargements do not always make shapes bigger . The shape can be made smaller if the scale factor is between 0 and 1.

Define the scale factor of enlargement .

The scale factor tells you how many times bigger each edge of the enlarged image will be compared to the corresponding edge on the original object.

To get full marks, what information do you need to give when describing an enlargement in an exam question?

When describing an enlargement , you need to: state that the transformation is an enlargement state the scale factor state the coordinates of the centre of enlargement

True or False? The centre of enlargement determines the position of the enlarged shape for a given scale factor.

True. The centre of enlargement determines the position of the enlarged shape for a given scale factor.

True or False? One of the corners of the enlarged shape is always on the centre of enlargement.

False. One of the corners of the enlarged shape does not have to be on the centre of enlargement.

How do you enlarge a shape?

To enlarge a shape: Count/measure the distances from the centre to a corner Multiply the distances by the scale factor Count the new distances from the centre of enlargement Repeat this for all the corners Join the corners together to form the enlarged shape

True or False? If you draw a straight line that passes through a corner on the original shape and the corresponding corner on the enlarged shape, then that line will pass through the centre of enlargement .

True. If you draw a straight line that passes through a corner on the original shape and the corresponding corner on the enlarged shape, then that line will pass through the centre of enlargement . This can be used to find the centre of enlargement or check your enlargements. These lines are sometimes called rays.

How do you find the scale factor of an enlargement?

To find the scale factor of an enlargement, divide the length of any side on the enlarged shape by the length of the corresponding side on the original shape.

How do you find the centre of enlargement ?

To find the centre of enlargement , draw straight lines that pass through a corner on the original shape and the corresponding corner on the enlarged shape. The point of intersection of these lines will be the centre of enlargement.

True or False? The scale factor of enlargement is the scale factor between the area of the original shape and the area of the enlarged shape.

False. The scale factor of enlargement is not the scale factor between the area of the original shape and the area of the enlarged shape. It is the scale factor of their lengths, not their areas.

True or False? If you reflect a shape in a given line and then reflect the image in the same line, you get back to the original shape .

True. If you reflect a shape in a given line and then reflect the image in the same line, you get back to the original shape .

A is rotated 270° clockwise about (0, 0) and then rotated 90° anticlockwise about (0, 0). Which single transformation describes this sequence of rotations?

A is rotated 270° clockwise about (0, 0) and then rotated 90° anticlockwise about (0, 0). This sequence of rotations can be described by the single transformation that is a rotation of 180° about (0, 0) .

True or False? Reflecting a shape in the x-axis and then rotating it 90° clockwise about (0, 0) is the same overall transformation as rotating the shape 90° clockwise about (0, 0) and then reflecting it in the x-axis.

False. Reflecting a shape in the x-axis and then rotating it 90° clockwise about (0, 0) is not the same overall transformation as rotating the shape 90° clockwise about (0, 0) and then reflecting it in the x-axis. In general, the order of transformations matters.

IGCSEMaths A: HigherEdexcelFlashcards

Transformations (Edexcel IGCSE Maths A)

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Define the term translation.

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Define the term translation.
A translation is when a shape is moved. Its position changes but its size, shape and orientation stay the same.
What do you use to describe how a shape is moved horizontally and vertically by a translation?
You use a vector in the form $(\begin{matrix} x \\ y \end{matrix})$ to describe a translation, $x$ describes the horizontal movement and $y$ describes the vertical movement.
True or False?
The vector $(\begin{matrix} 2 \\ 3 \end{matrix})$ means 3 units to the right and 2 units up.
False.
The vector $(\begin{matrix} 2 \\ 3 \end{matrix})$ means 2 units to the right and 3 units up.
The top number is horizontal and the bottom number is vertical.
True or False?
The vector $(\begin{matrix} - 2 \\ 0 \end{matrix})$ means 2 units to the left.
True.
The vector $(\begin{matrix} - 2 \\ 0 \end{matrix})$ means 2 units to the left.
True or False?
The vector $(\begin{matrix} 0 \\ - 3 \end{matrix})$ means 3 units up.
False.
The vector $(\begin{matrix} 0 \\ - 3 \end{matrix})$ means 3 units down.
If the bottom number is negative it goes down.
How do you translate a shape?
Move each corner according to the vector. Join the new corners together to make the translated shape.
True or False?
When you translate a shape, it should not overlap with the original shape.
False.
When you translate a shape, it can overlap with the original shape.
To get full marks, what information do you need to give when describing a translation in an exam question?
When describing a translation, you need to:
- state that the transformation is a translation
- state the vector
Define the term reflection.
A reflection is when a shape is flipped about a line of symmetry. Its orientation changes and its position could change but its size stays the same.
True or False?
A reflection in the line $y = 0$ is always the same as a reflection in the y-axis.
False.
A reflection in the line $y = 0$ is not always the same as a reflection in the y-axis. However, a reflection in the line $y = 0$ is always the same as a reflection in the x-axis.
True or False?
The line of reflection will always be horizontal or vertical.
False.
The line of reflection will not always be horizontal or vertical. It could be diagonal such as $y = x$ or $y = - x$ .
Which points do not change when reflected?
The points on the line of reflection do not change when reflected.
How do you reflect a shape about a line of reflection?
To reflect a shape, reflect each corner separately.
- Count or measure the perpendicular distance from a corner to the line of reflection
- Repeat this distance on the other side of the line
- Label the new corner
- Join all the corners up to form the reflected shape
To get full marks, what information do you need to give when describing a reflection in an exam question?
When describing a reflection, you need to:
- state that the transformation is a reflection
- state the equation of the line of reflection
Define the term rotation.
A rotation is when a shape is turned about a point. Its position could change but its size stays the same.
True or False?
A rotation 90^°clockwise is the same as a rotation 270^° anticlockwise.
True.
A rotation 90^°clockwise is the same as a rotation 270^° anticlockwise.
True or False?
You must state the direction of the rotation when the angle is 180°.
False.
You do not need to state the direction of the rotation when the angle is 180°. 180° clockwise is the same as 180° anticlockwise.
To get full marks, what information do you need to give when describing a rotation in an exam question?
When describing a rotation, you need to:
- state that the transformation is a rotation
- state the angle and direction of the rotation
- state the position of the centre of the rotation
How do you rotate a shape about a centre of rotation?
To rotate a shape:
- Trace over the original shape
- Put your pencil on the centre of rotation
- Rotate the tracing paper by the given angle and in the given direction
- Draw the rotated shape as indicated by the tracing paper
True or False?
The centre of rotation can be inside the original shape.
True.
The centre of rotation can be inside the original shape.
Define the term enlargement.
An enlargement is when a shape is stretched (or shrunk) both horizontally and vertically by the same factor.
True or False?
Enlargements always make shapes bigger.
False.
Enlargements do not always make shapes bigger. The shape can be made smaller if the scale factor is between 0 and 1.
Define the scale factor of enlargement.
The scale factor tells you how many times bigger each edge of the enlarged image will be compared to the corresponding edge on the original object.
To get full marks, what information do you need to give when describing an enlargement in an exam question?
When describing an enlargement, you need to:
- state that the transformation is an enlargement
- state the scale factor
- state the coordinates of the centre of enlargement
True or False?
The centre of enlargement determines the position of the enlarged shape for a given scale factor.
True.
The centre of enlargement determines the position of the enlarged shape for a given scale factor.
True or False?
One of the corners of the enlarged shape is always on the centre of enlargement.
False.
One of the corners of the enlarged shape does not have to be on the centre of enlargement.
How do you enlarge a shape?
To enlarge a shape:
- Count/measure the distances from the centre to a corner
- Multiply the distances by the scale factor
- Count the new distances from the centre of enlargement
- Repeat this for all the corners
- Join the corners together to form the enlarged shape
True or False?
If you draw a straight line that passes through a corner on the original shape and the corresponding corner on the enlarged shape, then that line will pass through the centre of enlargement.
True.
If you draw a straight line that passes through a corner on the original shape and the corresponding corner on the enlarged shape, then that line will pass through the centre of enlargement.
This can be used to find the centre of enlargement or check your enlargements.
These lines are sometimes called rays.
How do you find the scale factor of an enlargement?
To find the scale factor of an enlargement, divide the length of any side on the enlarged shape by the length of the corresponding side on the original shape.
How do you find the centre of enlargement?
To find the centre of enlargement, draw straight lines that pass through a corner on the original shape and the corresponding corner on the enlarged shape. The point of intersection of these lines will be the centre of enlargement.
True or False?
The scale factor of enlargement is the scale factor between the area of the original shape and the area of the enlarged shape.
False.
The scale factor of enlargement is not the scale factor between the area of the original shape and the area of the enlarged shape. It is the scale factor of their lengths, not their areas.
True or False?
If you reflect a shape in a given line and then reflect the image in the same line, you get back to the original shape.
True.
If you reflect a shape in a given line and then reflect the image in the same line, you get back to the original shape.
Shape A is translated by the vector $(\begin{matrix} 2 \\ - 4 \end{matrix})$ to create shape B.
Which translation vector takes shape B back to shape A?
Shape A is translated by the vector $(\begin{matrix} 2 \\ - 4 \end{matrix})$ to create shape B.
The vector $(\begin{matrix} - 2 \\ 4 \end{matrix})$ takes shape B back to shape A.
To undo a translation, you multiply the vector by -1.
True or False?
If A is transformed to B by an enlargement about (0, 0) using a scale factor of 2, then an enlargement about (0, 0) using a scale factor of -2 transforms B to A.
False.
If A is transformed to B by an enlarged about (0, 0) using a scale factor of 2, then an enlargement about (0, 0) using a scale factor of -2 does not transform B to A.
The scale factor needs to be the reciprocal to undo an enlargement. The scale factor would be $\frac{1}{2}$ .
A is rotated 270° clockwise about (0, 0) and then rotated 90° anticlockwise about (0, 0).
Which single transformation describes this sequence of rotations?
A is rotated 270° clockwise about (0, 0) and then rotated 90° anticlockwise about (0, 0).
This sequence of rotations can be described by the single transformation that is a rotation of 180° about (0, 0).
True or False?
Reflecting a shape in the x-axis and then rotating it 90° clockwise about (0, 0) is the same overall transformation as rotating the shape 90° clockwise about (0, 0) and then reflecting it in the x-axis.
False.
Reflecting a shape in the x-axis and then rotating it 90° clockwise about (0, 0) is not the same overall transformation as rotating the shape 90° clockwise about (0, 0) and then reflecting it in the x-axis.
In general, the order of transformations matters.

1. Numbers & the Number System

2. Equations, Formulae & Identities

3. Sequences, Functions & Graphs

4. Geometry & Trigonometry

5. Vectors & Transformation Geometry

6. Statistics & Probability