G7, G8, G24Transformations

Edexcel GCSE Maths (1MA1), Higher tier · Geometry and measures

Practise Transformations. 2 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.

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Shape A is rotated to give shape B. Jo describes the transformation as 'a rotation of 90°'. Jo's description is not complete. Write down the two other pieces of information that are needed to describe the rotation fully.: The direction (clockwise or anticlockwise) and the centre of rotation.

Sample questions

Written for this site in the style of Edexcel exam questions. They are not taken from real past papers.

Question 1Easy2 marks

Shape A is rotated to give shape B.
Jo describes the transformation as 'a rotation of 90°'.
Jo's description is not complete. Write down the two other pieces of information that are needed to describe the rotation fully.[2]

Show the answer and mark scheme

Answer: The direction (clockwise or anticlockwise) and the centre of rotation.

B1 for the direction of the rotation (clockwise or anticlockwise)
B1 for the centre of rotation

Worked solution: A rotation is described fully by its angle, its direction and its centre. Jo has given only the angle.

Question 2Medium4 marks

The grid shows triangle A.

[object Object]

(a) On the grid, draw the image of triangle A after a rotation of 180° about the point (0, 0).
Label the image B.[2]

(b) On the grid, draw the image of triangle A after a reflection in the line \(y = -x\).
Label the image C.[2]

Show the answer and mark scheme

(a) Answer: Triangle B with vertices (5, −1), (5, −4), (3, −2).

B2 for triangle B drawn with vertices (5, −1), (5, −4), (3, −2) (B1 for a rotation of 180° about a different centre, or a rotation about (0, 0) by the wrong angle or in the wrong direction)

Worked solution: Apply the transformation to each vertex of A: (−5, 1) \(\to\) (5, −1), (−5, 4) \(\to\) (5, −4), (−3, 2) \(\to\) (3, −2).

(b) Answer: Triangle C with vertices (−1, 5), (−4, 5), (−2, 3).

B2 for triangle C drawn with vertices (−1, 5), (−4, 5), (−2, 3) (B1 for a reflection of A in the line \(y = x\) (the wrong diagonal), or for triangle C with at least two vertices correct)

Worked solution: Reflecting in \(y = -x\) maps \((x, y) \to (-y, -x)\): (−5, 1) \(\to\) (−1, 5), (−5, 4) \(\to\) (−4, 5), (−3, 2) \(\to\) (−2, 3).

Question 3Hard3 marks

Triangle T is reflected in the line \(y = x\) to give triangle U.
Triangle U is then reflected in the \(x\)-axis to give triangle V.
Describe fully the single transformation that maps triangle T onto triangle V.
You may use a point such as \((3, 1)\) to help you.[3]

Show the answer and mark scheme

Answer: A rotation of 90° clockwise about the origin \((0, 0)\).

M1 for following a point through both reflections, e.g. \((3, 1) \to (1, 3) \to (1, -3)\), or \((x, y) \to (y, x) \to (y, -x)\)
B1 for rotation 90° clockwise (or 270° anticlockwise)
B1 for centre \((0, 0)\)

Worked solution: Reflecting in \(y = x\) swaps the coordinates, \((x, y) \to (y, x)\). Reflecting in the \(x\)-axis changes the sign of \(y\): \((y, x) \to (y, -x)\).
\((x, y) \to (y, -x)\) is a rotation of 90° clockwise about the origin (e.g. \((3, 1) \to (1, -3)\), and \((0, 0)\) is fixed).

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