GCSE-ready- Home
- Lessons
- KS3 Mathematics
- Transformations
Transformations
🎬 The doodle video for this lesson is coming soon. Subscribe on YouTube to see it first.
Transformations move or resize shapes. There are four you need to know, and each must be described fully.
Translation, reflection, rotation
Translation: slide. Describe it by how far right or left and up or down.
Reflection: flip in a mirror line, such as the x-axis, the y-axis, y = x or x = 2.
Rotation: turn. Give the angle, the direction (clockwise or anticlockwise) and the centre.
These three give congruent images: same shape, same size.
Reflection: flip in a mirror line, such as the x-axis, the y-axis, y = x or x = 2.
Rotation: turn. Give the angle, the direction (clockwise or anticlockwise) and the centre.
These three give congruent images: same shape, same size.
Enlargement
An enlargement changes the size by a scale factor from a centre.
Scale factor 3: every length is 3 times as long. A 2 cm by 5 cm rectangle becomes 6 cm by 15 cm.
From the origin, multiply the coordinates: (3, −1) with scale factor 2 goes to (6, −2).
The image is similar: same shape, angles unchanged, different size.
Scale factor 3: every length is 3 times as long. A 2 cm by 5 cm rectangle becomes 6 cm by 15 cm.
From the origin, multiply the coordinates: (3, −1) with scale factor 2 goes to (6, −2).
The image is similar: same shape, angles unchanged, different size.
Coordinate rules
Reflect in the x-axis: (x, y) → (x, −y).
Reflect in the y-axis: (x, y) → (−x, y).
Rotate 90° clockwise about the origin: (x, y) → (y, −x).
Reflect in the y-axis: (x, y) → (−x, y).
Rotate 90° clockwise about the origin: (x, y) → (y, −x).
Translate the point (2, 5) by 3 right and 4 down.
- x: 2 + 3 = 5
- y: 5 − 4 = 1
Answer: (5, 1)
Translations, reflections and rotations give congruent shapes. Enlargements give similar shapes. Always describe a transformation fully.
Check you have got it
Answer 7 quick questions with instant marking. If you get one wrong, GCSE-ready shows you why and gives you another go. It is free, and you do not need an account.