AQA · Mathematics · 8300
GCSE Maths: Invariant Points
Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Invariant Points (Corbettmaths Video 392), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
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What is an invariant point under a transformation?
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A point that maps to itself — its position is unchanged by the transformation.
How many invariant points does a translation by a non-zero vector have?
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None — every point moves by the same vector, so no point stays fixed.
Which points are invariant under a reflection?
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Only the points that lie on the mirror line.
Which point is invariant under a rotation (angle not a multiple of 360°)?
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Only the centre of rotation.
Which point is invariant under an enlargement with scale factor ≠ 1?
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Only the centre of enlargement.
How many vertices of a square are invariant when it is reflected in a line through two opposite vertices?
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Two — the vertices that lie on the mirror line.
Which single transformation leaves every point on side EF of a triangle invariant?
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A reflection in the line through E and F.
Which single transformation of a triangle makes exactly one vertex invariant?
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A rotation about that vertex (or an enlargement with that vertex as centre).
How do you find the invariant point of a combined (two-step) transformation?
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Apply both transformations in order and find the point that ends up back at its original position.
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