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Maths · Transformations and Similarity

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Maths · Edexcel Paper 2

Transformations and Similarity

Reflections and Translations

Reflecting shapes in mirror lines, translating them with column vectors, and describing each transformation fully.

  • Transformation A change in the position or size of a shape.
  • Object The original shape before a transformation.
  • Image The shape after a transformation.
Triangle A reflected in the line x equals 1 to give triangle B on the other side of the line.

Rotations

Rotating shapes about a centre, describing a rotation fully, and finding the centre of a rotation.

  • Rotation A transformation that turns a shape about a fixed point.
  • Centre of rotation The fixed point about which a shape is turned.
  • Clockwise The direction of the hands of a clock.
Triangle A rotated 90 degrees clockwise about the origin to give triangle B.

Enlargements

Enlarging shapes by whole-number, fractional and negative scale factors, and describing an enlargement fully.

  • Enlargement A transformation that changes the size of a shape by a scale factor.
  • Scale factor The number by which every length of a shape is multiplied.
  • Centre of enlargement The fixed point from which an enlargement is measured.
Triangle A enlarged by scale factor 2 from the centre (1, 1) to give a triangle B twice as big.

Combined Transformations (Higher tier)

Carrying out one transformation after another, finding the single equivalent transformation, and spotting invariant points.

  • Combined transformation One transformation followed by another.
  • Invariant Not changed by a transformation.
  • Invariant point A point that stays in the same place under a transformation.
Triangle A reflected in the x-axis to give B, then in the y-axis to give C, which is A rotated through 180 degrees about the origin.

Congruence and Similarity

Proving triangles congruent, finding missing lengths in similar shapes, and using scale factors for length, area and volume.

  • Congruent Exactly the same size and shape.
  • Similar The same shape, with corresponding sides in the same ratio.
  • Scale factor The ratio of corresponding lengths in similar shapes.
Two triangles with two pairs of equal sides and the equal angle between them, so they are congruent by SAS.