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GCSE Mathematics · key term
A point that remains in the same position under a transformation.
Used by AQA, Edexcel and OCR
Specification A13, G8 · Paper 1, Paper 2, Paper 3
A point that remains in the same position under a particular transformation.
A point that finishes in exactly the same position after a transformation or sequence of transformations.
If asked for invariant points, check which points stay in exactly the same place. A shape landing on itself does not mean its vertices are invariant.
Distinguish an invariant property from an invariant point: a length may stay unchanged even though both endpoints move.
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Specification G8 · Paper 1, Paper 2, Paper 3
A point whose image is in exactly the same position as the original point.
Revise: InvarianceIn a combination, judge invariant points from the overall result, not from either step alone: two opposite translations leave every point invariant, even though each step moves every point.
Specification 9.01a, 9.01b, 9.01d · Paper 1 (Foundation), Paper 2 (Foundation), Paper 3 (Foundation), Paper 4 (Higher), Paper 5 (Higher), Paper 6 (Higher)
A point whose image occupies exactly the same position as the original point.