A-Level Further Maths · Further Pure
Linear Transformations
What is it
A linear transformation uses a matrix to move every point in a plane or space according to a consistent rule, such as a rotation, reflection, or enlargement — preserving straight lines and the origin's position.
Why it matters
Linear transformations connect matrices directly to geometry, and this exact mathematics — representing transformations as matrices — is precisely what powers computer graphics, from video game rendering to CAD software.
Exam tip
Memorise the standard transformation matrices (rotation, reflection in the axes, enlargement) rather than deriving them each time — recognising a transformation matrix on sight saves significant time in the exam.
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