Combination of Transformations (Edexcel IGCSE Maths A (Modular))

Combination of Transformations

What do I need to know about combined transformations?

• Combined transformations are when more than one transformation is performed, one after the other

• In many cases, two transformations can be equivalent to one alternative single transformation

  • Finding this single transformation is a common exam question

• Rotation

  • Requires an angle, direction and centre of rotation

  • It is usually easy to tell the angle from the orientation of the image

  • You can use trial and error and tracing paper to find the centre of enlargement

• Reflection

  • A reflection will be in a mirror line which can be vertical (x = k), horizontal (y = k) or diagonal (y = mx + c)

  • Points on the mirror line do not move

  • It is possible for a mirror line to pass through the object

• Translation

  • A translation is a movement which does not change the orientation or size of the shape, it simply moves location

  • A translation is described by a vector in the form 

    • This represents a movement of x units to the right and y units vertically upwards

What are common combinations of transformations?

• A combination of two reflections can be the same as a single rotation

  • One reflection using the line and the other using the line 

  • This is the same as a 180° rotation about the centre 

• The order of the combination can be important to the overall effect

  • A reflection in the line y = x followed by a reflection in the x-axis is the same as a 90° rotation clockwise about the origin

  • A reflection in the x-axis followed by a reflection in the line y = x is the same as a 90° rotation anticlockwise about the origin

How do I undo a transformation to get back to the original shape?

• After transforming shape A to make shape B you could be asked to describe the transformation that maps B to A