Transformations
Transformations move or change shapes on a coordinate grid. In GCSE Maths, you need to recognise, perform and describe translations, reflections, rotations and enlargements.
The four main transformations are:
translation, reflection, rotation and enlargement.
Translation
A translation moves a shape without turning it or changing its size. It is usually described using a vector.
Example 1: Translate a point
Translate the point (2, 3) by the vector (4, -1).
Add 4 to the x-coordinate and subtract 1 from the y-coordinate:
(2 + 4, 3 - 1) = (6, 2)
The translated point is (6, 2).
Reflection
A reflection flips a shape in a mirror line. To describe a reflection fully, give the equation of the mirror line.
Example 2: Reflect in the x-axis
Reflect the point (3, 5) in the x-axis.
The x-coordinate stays the same. The y-coordinate changes sign.
(3, 5) → (3, -5)
Example 3: Reflect in the y-axis
Reflect the point (-4, 2) in the y-axis.
The y-coordinate stays the same. The x-coordinate changes sign.
(-4, 2) → (4, 2)
Rotation
A rotation turns a shape around a centre of rotation. To describe a rotation fully, give the angle, direction and centre of rotation.
Example 4: Describe a rotation
A shape has been turned 90° clockwise around the origin.
A full description is:
Rotation 90° clockwise about (0, 0)
Enlargement
An enlargement changes the size of a shape. To describe an enlargement fully, give the scale factor and centre of enlargement.
Example 5: Enlarge by scale factor 2
Enlarge a point from centre (0, 0) by scale factor 2.
The point (3, 4) becomes:
(6, 8)
How to describe transformations fully
Translation: give the vector.
Reflection: give the mirror line.
Rotation: give angle, direction and centre.
Enlargement: give scale factor and centre.
A common mistake is giving an incomplete description. For example, saying “rotation 90°” is not enough. You must also give direction and centre of rotation.
When describing transformations, imagine the examiner is trying to recreate the exact movement. Give enough information so there is only one possible answer.
Video explanation
A short Worthing Maths Tutor video explanation for transformations can be embedded here later to improve student engagement and time on page.
Practice questions
- Translate (1, 4) by the vector (3, 2).
- Reflect (5, 6) in the x-axis.
- Reflect (-3, 7) in the y-axis.
- What information is needed to describe a rotation fully?
- What information is needed to describe an enlargement fully?
Answers
- (4, 6)
- (5, -6)
- (3, 7)
- Angle, direction and centre of rotation
- Scale factor and centre of enlargement
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