EDEXCEL GCSE HIGHER MATHS - What are Transformations (Translations, Reflections, Rotations, Enlargements)

Edexcel GCSE Higher Maths - Transformations

Transformations are ways of moving or changing the size and shape of a shape. There are four main types of transformations:

1. Translations:

• Definition: A translation moves every point of a shape the same distance and in the same direction.
• How to describe: Use a vector to represent the movement. For example, the vector ( 3 2 ) means move 3 units to the right and 2 units up.
• Notation: T ( 3 2 )
• Example:

Original shape: A(1,2), B(3,2), C(3,4) Translation: T ( 2 1 ) Translated shape: A'(3,3), B'(5,3), C'(5,5)

2. Reflections:

• Definition: A reflection flips a shape over a line (the mirror line).
• How to describe: State the mirror line. For example, "Reflect in the x-axis."
• Notation: M y = 0 (for reflection in the x-axis)
• Example:

Original shape: A(1,2), B(3,2), C(3,4) Reflection: M y = 0 Reflected shape: A'(1,-2), B'(3,-2), C'(3,-4)

3. Rotations:

• Definition: A rotation turns a shape around a fixed point (the centre of rotation).
• How to describe: State the centre of rotation, the angle of rotation (clockwise or anticlockwise), and the direction of rotation (clockwise or anticlockwise). For example, "Rotate 90 degrees clockwise about the point (2,1)."
• Notation: R 90° (2,1)
• Example:

Original shape: A(1,2), B(3,2), C(3,4) Rotation: R 90° (0,0) Rotated shape: A'(-2,1), B'(-2,3), C'(-4,3)

4. Enlargements:

• Definition: An enlargement makes a shape bigger or smaller by a scale factor.
• How to describe: State the centre of enlargement and the scale factor. For example, "Enlarge by a scale factor of 2 with centre (0,0)."
• Notation: E 2 (0,0)
• Example:

Original shape: A(1,2), B(3,2), C(3,4) Enlargement: E 2 (0,0) Enlarged shape: A'(2,4), B'(6,4), C'(6,8)

Important points:

• The order of transformations matters. For example, reflecting then translating is different from translating then reflecting.
• You can combine different types of transformations. For example, you can translate a shape and then rotate it.
• Understanding transformations is essential for many geometric problems, including finding the area and perimeter of shapes, proving congruence and similarity, and solving problems in coordinate geometry.

Practice questions:

1. Describe the transformation that maps triangle ABC onto triangle A'B'C'.
2. Draw the image of shape P after it has been reflected in the line y=x.
3. Find the centre of enlargement for the enlargement that maps triangle DEF onto triangle D'E'F'.

Tips for success:

• Learn the definitions of each type of transformation.
• Practice describing and performing transformations.
• Understand the relationship between transformations and geometric properties.
• Use your knowledge of transformations to solve problems.