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Mathematics 05807.1 Transformations

Transformations

Translate, reflect, rotate and enlarge a shape, with the full description an examiner wants shown alongside.

  • Translation vectors
  • Mirror lines
  • Centre and angle of rotation
  • Scale factor

Full description — what the exam wants

Translation by the vector (3, 2).

Predict

Which of these transformations changes the size of the shape?

Experiment

  1. 1Translate the shape by (3, 2), then read the full description. Note that a vector, not a distance, is required.
  2. 2Reflect in the y-axis and then in y = x, and see that the order matters.
  3. 3Rotate by 90° and then by −90°, and check the description names the angle, the direction and the centre.
  4. 4Set the enlargement scale factor to −2 and describe what a negative scale factor does.

Explain

Marks in these questions are for the full description, and each type has its own required parts:

  • Translation — name it and give the column vector.
  • Reflection — name it and give the equation of the mirror line.
  • Rotation — name it and give the angle, the direction and the centre.
  • Enlargement — name it and give the scale factor and the centre.

Missing any one of those parts loses a mark, and it is the commonest way to drop marks in the topic. “Rotation of 90°” is not a full description; “rotation of 90° anticlockwise about (0, 0)” is.

A negative scale factor puts the image on the opposite side of the centre and turns it through 180°, which is why it looks upside down.