Transformations
Transformations describe four ways of moving or resizing a shape on a coordinate grid: translation (sliding), reflection (flipping in a mirror line), rotation (turning about a centre) and enlargement (making a shape bigger or smaller from a centre of enlargement). GCSE questions ask you to both perform and fully describe each transformation.
Method
- For a translation, move every point of the shape by the same vector, right or left and up or down.
- For a reflection, flip the shape over the mirror line so each point stays the same distance from the line, on the opposite side.
- For a rotation, turn the shape by the given angle and direction about the centre of rotation, using tracing paper if needed.
- For an enlargement, multiply the distance of each vertex from the centre by the scale factor to find the new vertices.
- When describing a transformation, always state the type first, then all the required details: vector, or mirror line, or angle/direction/centre, or scale factor/centre.
Worked example
Triangle P has vertices at (1, 1), (1, 3) and (4, 1). Triangle P is reflected in the y-axis to give triangle P'. Find the coordinates of the vertices of triangle P'.
- Reflecting in the y-axis negates the x-coordinate of each point and keeps the y-coordinate the same.
- (1, 1) becomes (-1, 1).
- (1, 3) becomes (-1, 3).
- (4, 1) becomes (-4, 1).
- Final answer: P' has vertices (-1, 1), (-1, 3), (-4, 1).
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a GCSE Maths exam paper, with a full mark scheme.
Shape M has vertices at (-4, 2), (-4, 5) and (-2, 2). Shape M is translated by the vector (3, -4) to give shape N. Find the coordinates of the vertices of shape N.
Describe fully the single transformation that maps triangle X, with vertices (1, 1), (1, 4) and (3, 1), onto triangle Y, with vertices (1, -1), (1, -4) and (3, -1).
Triangle T has vertices at (1, 1), (2, 1) and (1, 3). Triangle T is enlarged by scale factor 4, centre (0, 0), to give triangle T'. Find the coordinates of the vertices of T'.
See real past-paper questions on transformations, organised by topic with official mark schemes →
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