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Invariant Points

Maths: Edexcel GCSE Higher, topic 4.19.1

Invariant Points

Points are invariant (unchanged) if they remain the same before and after a transformation. Types of transformation include reflection, rotation, translation and enlargement.

Rotation

Rotation

  • The only point of invariance under a rotation is the centre of rotation.
Reflection

Reflection

  • All points on the line of reflection are invariant.
Enlargement

Enlargement

  • The only point of invariance under an enlargement is the centre of enlargement.
Translation

Translation

  • No points are invariant under a translation.

Test yourself on Invariant Points

  • If we reflect the blue triangle in the x axis, what colour triangle do we get?

  • If we reflect the blue triangle in the y axis, what colour triangle do we get?

  • If we reflect the blue triangle in the line y = x, what colour triangle do we get?

  • If we reflect the blue triangle in the line y = x + 1, what colour triangle do we get?

  • What do we call points that remain the same before and after a transformation?

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