Transformations

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infoWhy this? Describing transformations fully develops precise geometric language and reasoning about congruence, similarity, orientation, and invariance. General mirror lines and varied enlargement factors also strengthen links between algebra and coordinate geometry.

scheduleWhy now? Years 7 and 8 established how to perform the main transformations and work from specified centres and lines. We now focus on identifying and describing transformations, including reflections in y = mx + c and enlargements with a wider range of scale factors.

A translation moves every point of a shape the same distance in the same direction and can be described using a column vector.
A rotation turns a shape about a fixed point, called the centre of rotation, through a specified angle and direction (clockwise or anticlockwise).
To describe a rotation fully, the centre of rotation, the angle of rotation (usually `90^\circ`, `180^\circ`, or `270^\circ`), and the direction must be specified.
A reflection maps each point of a shape to an image on the opposite side of a given line, called the mirror line, at the same perpendicular distance from the line.
The equation of a straight line in the form `y = mx + c` represents a mirror line for reflection, where `m` is the gradient and `c` is the `y`-intercept.
An enlargement changes the size of a shape by a scale factor, relative to a fixed point called the centre of enlargement.
To describe an enlargement fully, you must specify the centre of enlargement and the scale factor, which may be positive, negative, greater than 1, between 0 and 1, or negative.

rocket_launchYou must be able to

Describe fully the translation that maps one object onto another using a column vector, by calculating the horizontal and vertical distances between corresponding points.
Describe fully a rotation that maps one object onto another, by identifying the centre of rotation, the angle, and the direction (clockwise or anticlockwise).
Reflect a shape in a line of the form `y = mx + c` by constructing perpendiculars from points on the shape to the line and marking points the same distance on the other side.
Describe fully a reflection that maps one object onto another, by identifying the equation of the mirror line.
Describe fully the enlargement that maps one object onto another, by identifying the centre of enlargement and calculating the scale factor.

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