Sheet № 57 · Foundation + Higher · AQA · Edexcel · OCR
Transformations: Reflection, Rotation, Translation
Transformations are a key part of GCSE Maths, tested at both Foundation and Higher tiers on AQA, Edexcel, and OCR. You need to be able to perform and describe three types of transformation: reflections, rotations, and translations. Each one moves a shape to a new position in a specific way, and the image is always congruent to the origina
§Key definitions
Tip:
For 90° clockwise rotation about the origin, the point (x, y) maps to (y, −x). For 90° anticlockwise, it maps to (−y, x). For 180°, it maps to (−x, −y).
Question:
Triangle P has vertices at (1, 1), (1, 4), and (3, 1). Translate triangle P by the vector (4 over −2). Write down the coordinates of the image.
Answer:
The image has vertices at (5, −1), (5, 2), and (7, −1).
Question 1:
Reflect the point (3, 5) in the x-axis.
Question 2:
Rotate the point (2, 3) by 90° clockwise about the origin.
§Formulas to memorise
The line of reflection (e.g. x = 2, y = −1, y = x, the x-axis, the y-axis).
Tip:: For 90° clockwise rotation about the origin, the point (x, y) maps to (y, −x). For 90° anticlockwise, it maps to (−y, x). For 180°, it maps to (−x, −y).
Worked example
Triangle P has vertices at (1, 1), (1, 4), and (3, 1). Translate triangle P by the vector (4 over −2). Write down the coordinates of the image.
Working:
⚠ Common mistakes
- ✗Incomplete descriptions. Saying "a rotation of 90°" without giving the direction and centre loses marks. Always give every required detail.
- ✗Confusing clockwise and anticlockwise. 90° clockwise is the same as 270° anticlockwise. Be consistent and match the question's language.
- ✗Reflecting at an angle to the mirror line instead of perpendicular. Always measure the shortest (perpendicular) distance to the line.
- ✗Mixing up the vector components. The top number is horizontal (x-direction) and the bottom number is vertical (y-direction). Positive x is right; positive y is up.
- ✗Saying "moved" instead of "translated". Use the correct mathematical term. Similarly, do not say "flipped" — say "reflected."
✦ Exam tips
- →Use tracing paper for rotations. Place it over the shape, hold your pencil on the centre of rotation, and turn the paper.
- →When describing, name the transformation first — "This is a reflection in..." Always use the precise mathematical name.
- →For reflections in diagonal lines (y = x or y = −x), swap the coordinates. For y = x: (a, b) → (b, a). For y = −x: (a, b) → (−b, −a).
- →Check your image is congruent. If the image is a different size, you have made an error (or the transformation is an enlargement, which is a different topic).
- →Label the image with a prime symbol (A → A') to avoid confusion between original and image.