📏
Geometry & Measures · Higher

Transformations

The four transformations are: reflection, rotation, translation and enlargement. At Higher tier you must describe them fully, apply them, and work with negative scale factors for enlargements. Combined transformations may also be examined.

🔑

Key facts to remember

  • 1Reflection: needs the mirror line equation (e.g. y = x, x = 2).
  • 2Rotation: needs the centre of rotation, angle, and direction (clockwise or anticlockwise).
  • 3Translation: described by a column vector (x/y) — positive x moves right, positive y moves up.
  • 4Enlargement: needs the centre of enlargement and scale factor. Scale factor = image length ÷ original length.
  • 5Negative scale factor: the image is on the opposite side of the centre and inverted.
  • 6Transformations that preserve shape and size (isometries): reflection, rotation, translation.
✍️

Worked examples

Example 1

Describe fully the single transformation that maps triangle A onto triangle B, where A has vertices (1,1),(3,1),(3,4) and B has vertices (−1,1),(−3,1),(−3,4).

Working

  1. Compare the x-coordinates: each x has been negated (1→−1, 3→−3). y-values unchanged.
  2. This is a reflection in the y-axis (the line x = 0).
  3. Check: reflecting (1,1) in x = 0 gives (−1,1) ✓
AnswerReflection in the y-axis (x = 0).
Example 2

Enlarge triangle T with vertices (2,1),(4,1),(4,3) by scale factor −2 about centre (1,1).

Working

  1. Find vector from centre to each vertex, multiply by −2.
  2. (2,1)→(1,0) vector, ×(−2) = (−2,0), image point: (1−2, 1+0) = (−1,1)
  3. (4,1)→(3,0) vector, ×(−2) = (−6,0), image point: (1−6, 1+0) = (−5,1)
  4. (4,3)→(3,2) vector, ×(−2) = (−6,−4), image point: (1−6, 1−4) = (−5,−3)
  5. Image is on opposite side of centre, inverted.
AnswerImage vertices: (−1,1), (−5,1), (−5,−3).
⚠️

Common mistakes

✗Giving an incomplete description — always state all required information.
✗Confusing clockwise and anticlockwise for rotations.
✗For enlargements, measuring from the wrong centre.
✗Not inverting the image when using a negative scale factor.
🎯

Exam tips

✓For "describe fully": reflection needs line, rotation needs centre + angle + direction, enlargement needs centre + scale factor.
✓Use tracing paper in exams for rotations and reflections.
✓For negative scale factors, draw lines through the centre of enlargement and go to the other side.
✓A scale factor between −1 and 0 gives a smaller inverted image.

Ready to test yourself on Transformations?

Get AI-marked practice questions on exactly this subtopic.

Practice this topic →
← All topicsDashboard

▶️ Watch on YouTube

Free video lessons

Click a topic to search

▶transformations GCSE Higher maths▶rotation reflection translation enlargement GCSE▶describing transformations GCSE Higher▶negative scale factor enlargement GCSE

Opens YouTube — pick any free GCSE video.