Topic: Reflections, Rotations, Translations and Enlargements; Congruence and Similarity (Higher - Unit 3)
| Specification References: G1.7h G1.7h Describe and transform 2D shapes using single or combined rotations, reflections, translations, or enlargements by a positive scale factor and distinguish properties that are preserved under particular transformations. Use positive fractional and negative scale factors. |
Candidates should be able to:
- describe and transform 2D shapes using single rotations
- understand that rotations are specified by a centre and an (anticlockwise) angle
- find a centre of rotation
- rotate a shape about the origin or any other point
- measure the angle of rotation using right angles
- measure the angle of rotation using simple fractions of a turn or degrees
- describe and transform 2D shapes using single reflections
- understand that reflections are specified by a mirror line
- identify the equation of a line of reflection
- describe and transform 2D shapes using single transformations
- understand that translations are specified by a distance and direction (using a vector)
- translate a given shape by a vector
- describe and transform 2D shapes using enlargements by a positive scale factor
- understand that an enlargement is specified by a centre and a scale factor
- enlarge a shape on a grid (centre not specified)
- draw an enlargement
- enlarge a shape using (0, 0) as the centre of enlargement
- enlarge shapes with a centre other than (0, 0)
- find the centre of enlargement
- describe and transform 2D shapes using combined rotations, reflections, translations, or enlargements
- distinguish properties that are preserved under particular transformations
- identify the scale factor of an enlargement of a shape as the ratio of the lengths of two corresponding sides
- understand that distances and angles are preserved under rotations, reflections and translations, so that any figure is congruent under any of these transformations
- recognise that enlargements preserve angle but not length
- identify the scale factor of an enlargement as the ratio of the length of any two corresponding line segments
- describe a translation
- use congruence to show that translations, rotations and reflections preserve length and angle, so that any figure is congruent to its image under any of these transformations
Notes
Foundation tier will be restricted to single transformations.
The direction of rotation will always be given.
Column vector notation should be understood.
Lines of symmetry on a Cartesian grid will be restricted to x = a, y = a, y = x, y = –x.
Scale factors for enlargements will be restricted to positive integers at Foundation tier.
Scale factors for enlargements can be positive fractional or negative at Higher tier.
Enlargements may be drawn on a grid, or on a Cartesian grid, where the centre of enlargement will always be at the intersection of two grid lines.
When describing transformations, the minimum requirement is:
Rotations described by centre, direction (unless half a turn) and an amount of turn (as a fraction of a whole or in degrees).
Reflection by a mirror line.
Translations described by a vector or a clear description such as 3 squares to the right, 5 squares down.
Candidates will always be asked to describe a single transformation but could be asked to do a combined transformation on a single shape.
Candidates could be asked to describe a single transformation equivalent to combination of transformations.