Transformations

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infoWhy this? Transformations develop spatial visualisation and precise reasoning about what changes and what remains invariant. Rotations, reflections, translations, and enlargements also connect geometry with coordinates, vectors, congruence, and similarity.

scheduleWhy now? Introducing the four main transformations in Year 7 establishes the vocabulary and accurate construction methods needed for later coordinate geometry. These foundations are subsequently extended to more complex mirror lines, centred enlargements, and full descriptions of transformations.

A rotation is a transformation that turns a shape about a fixed point, called the centre of rotation, through a specified angle and direction.
Common angles of rotation include `90^\circ`, `180^\circ`, and `270^\circ`, and these can be clockwise or anticlockwise.
The coordinates of points change in predictable ways under rotation about the origin; for example, `(x, y)` rotated `90^\circ` anticlockwise becomes `(-y, x)`.
A reflection is a transformation that flips a shape over a given line, called the mirror line.
The mirror line can be horizontal (`y = k`), vertical (`x = k`), or diagonal (`y = x` or `y = -x`).
Under reflection, each point and its image are the same perpendicular distance from the mirror line.
The x-axis (`y = 0`) and y-axis (`x = 0`) are common mirror lines on a coordinate grid.
A translation is a transformation that moves every point of a shape the same distance in the same direction.
Translations on a coordinate grid can be described using a column vector `\begin{pmatrix} a \\ b \end{pmatrix}`, where `a` is the movement in the x-direction and `b` is the movement in the y-direction.
An enlargement is a transformation that increases or decreases the size of a shape by a scale factor, relative to a fixed point called the centre of enlargement.
The scale factor of enlargement determines how much bigger or smaller the image is compared to the original object.
If the scale factor is greater than `1`, the image is an enlargement; if it is between `0` and `1`, the image is a reduction.
The centre of enlargement is the point from which all points are expanded or contracted.
The relationship between corresponding lengths in the object and its image is determined by the scale factor.

rocket_launchYou must be able to

Rotate a shape about a fixed point, including the origin and other coordinates, through a specified angle and direction on a grid. .
Reflect a shape in a horizontal or vertical line, such as `y = k` or `x = k`, on a grid. .
Reflect a shape in a diagonal line, such as `y = x` or `y = -x`, on a grid. .
Identify the equation of the mirror line that maps object A onto object B. .
Translate a shape on a grid from a worded description, such as ‘move 3 units right and 2 units up’. .
Translate a shape on a coordinate grid using a given column vector. .
Enlarge a shape by a given scale factor from a specified centre on a grid. .
Identify the scale factor of enlargement when given an object and its image. .

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