What you need to know
Check yourself against these “I can” statements.
- I can use a matrix to represent a linear transformation
- I can carry out reflections, rotations, enlargements and stretches with matrices
- I can find invariant points and invariant lines
- I can combine transformations by multiplying matrices
- I can work with linear transformations in three dimensions
- I can use an inverse matrix to undo a transformation
Practise this topic
7 resourcesLinear Transformations
Reflections in y = 0, x = 0, y = x and y = −x, rotations of multiples of 90°, stretches and enlargements, all about the origin. Describe the transformation from its matrix, write down the matrix, read both from a diagram, combine…
🧮 Tool3D Matrix Transformations
The unit cube and its image under a 3 × 3 matrix in 3D (drag to turn the view), with a slider t that morphs the cube from the identity to M. Change any entry with a slider (steps of 0.1, or whole numbers), − / + or by typing. The…
⬢ BlockbustersLinear Transformations Blockbusters
Blockbusters with the questions from the Linear Transformations worksheet: choose its levels for the ordinary hexagons and for the harder ★ ones. Show the answer and the worked solution, or play against the computer with multiple…
🕹️ Topic gameMatrix Mini Golf
Eighteen holes of top-down mini golf: aim the golfer, then stop the swinging power bar. KS3 turns by angles; AQA FM uses rotation matrices with 90° turns; A Level adds 45° (1/√2); Advanced takes any angle to 2 d.p. The last six…
🧩 ConnectionsMatrix Properties
2×2 (and on Hard, 3×3) matrices grouped by what they are: a given determinant, singular, rotation, reflection, enlargement, stretch, shear, symmetric or self-inverse.
🧩 ConnectionsMatrix Transformations
Each group is one transformation about the origin: its description, its 2×2 matrix and two ways of building it from two steps, as a product of two matrices or as “X, then Y” in words. Easy: reflections and rotations; Standard…
🧮 ToolThree Planes Explorer
Three equations in x, y and z drawn as three planes in 3D: drag to turn the view. Examples (a unique point, three parallel planes, coincident planes, two parallel planes cut by a third, a sheaf, a prism, and sheaf or prism? with…
Topics in this unit
- 7.2 Reflections and rotations · 1 resource
- 7.3 Enlargements and stretches · 1 resource
These are the pages for Linear transformations in the A Level Further Maths scheme of work, following Pearson Edexcel A Level Further Mathematics (9FM0). Open this topic in Mr Wells Maths to see it alongside the rest of the course.