Practise free

3.8 Transformations

Transformations

Everything on transformations that can come up in the WJEC GCSE Mathematics and Numeracy, in Unit 2 and Unit 3. Each skill below has the method, the mistake that costs the most marks, a worked example, and free practice marked the way WJEC marks it.

Practise transformations free

A worked example

Transformations · [1 mark]

The point P(1, −5) is rotated 180° about the origin. Write down the coordinates of its image.

  1. B1(−1, 5)

The exam skills (7)

Translations

  1. Count how far across: right is positive, left is negative.
  2. Count how far up: up is positive, down is negative.
  3. Write it as a column vector, across on top.

Watch out: Writing the numbers the wrong way round.

Worked example · Practise this skill free

Reflections

  1. The mirror line is exactly halfway between the shape and its image.
  2. Vertical lines are x = …; horizontal lines are y = ….
  3. Check a point: it should be the same distance from the line on both sides.

Watch out: Mixing up x = 2 (vertical) and y = 2 (horizontal).

Worked example · Practise this skill free

Transformations

  1. Reflect in the x-axis: change the sign of y.
  2. Reflect in the y-axis: change the sign of x.
  3. Rotate 180° about the origin: change both signs.

Watch out: Changing the wrong coordinate.

Worked example · Practise this skill free

Midpoints

  1. Add the two x-coordinates and halve.
  2. Add the two y-coordinates and halve.
  3. Write it as (x, y).

Watch out: Subtracting instead of adding, which finds half the distance, not the midpoint.

Worked example · Practise this skill free

Rotations

  1. Describe fully: the word rotation, the angle, the direction and the centre.
  2. Use tracing paper to test centres.
  3. Write all three facts.

Watch out: Leaving out the centre. "Describe fully" means three things.

Worked example · Practise this skill free

Enlargements

  1. Scale factor = image length ÷ object length.
  2. Join matching corners and extend the lines back: they meet at the centre.
  3. Write the word enlargement, the scale factor and the centre.

Watch out: Not giving the centre as coordinates.

Worked example · Practise this skill free

Combined transformations

  1. Try it on one point, e.g. (1, 2).
  2. Do the first transformation, then the second, to the result.
  3. See which single transformation takes the start to the end.

Watch out: Doing the transformations in the wrong order.

Worked example · Practise this skill free

Ready to try some?

Fresh questions every time, a hint aimed at your exact mistake, and the mark scheme after every answer. Free, no sign-up.

Start practising