IGCSE Mathematics: Transformations Practice Questions
Every transformation must be described with its name and its full defining information. A reflection needs the mirror line, a rotation needs centre, angle and direction, a translation needs a column vector, and an enlargement needs scale factor and centre.
Topic 7.1 of Cambridge IGCSE Mathematics 0580 loses more marks to incomplete descriptions than to wrong answers. Cambridge awards a mark for each required piece of information, so a rotation described without its centre cannot score full marks. The questions below list what each one needs.
What you need to know for Transformations
- ReflectionState the equation of the mirror line, for example y = x or x = 2. Each point moves to the same perpendicular distance on the other side.
- RotationState the centre of rotation, the angle and the direction, clockwise or anticlockwise. A rotation of 180 degrees needs no direction.
- TranslationState a column vector. The top number is the movement right and the bottom number is the movement up, with negatives for left and down.
- EnlargementState the scale factor and the centre of enlargement. A fractional scale factor makes the image smaller.
- Negative scale factorThe image appears on the opposite side of the centre and is inverted, as well as being scaled.
- One transformation onlyWhen asked to describe a single transformation, give exactly one. Describing it as two separate steps scores nothing.
IGCSE Mathematics Transformations questions and answers
4 exam-style questions written to the 0580 syllabus. Try each one on paper first, then open the worked answer to check your method against the marks.
State the information needed to describe each of the four transformations fully.
Show the worked answer
- A reflection requires the equation of the mirror line, such as y = x, x = 3 or the x-axis.
- A rotation requires the centre of rotation as coordinates, the angle, and the direction unless the angle is 180 degrees.
- A translation requires a column vector giving the horizontal and vertical movement.
- An enlargement requires the scale factor and the coordinates of the centre of enlargement.
A shape is reflected so that the point (3, 1) maps to (1, 3), and the point (5, 2) maps to (2, 5). Describe the transformation fully.
Show the worked answer
- Compare the coordinates: in each case the x and y values have swapped places.
- Swapping x and y is the effect of reflecting in the line y = x.
- Check with a third point if one is available, or verify that the midpoint of each object and image pair lies on the line y = x.
- The full description is a reflection in the line y = x.
Triangle A has vertices at (1, 1), (3, 1) and (1, 4). It is enlarged by scale factor 3, centre the origin. Find the coordinates of the image.
Show the worked answer
- With the centre of enlargement at the origin, multiply both coordinates of each point by the scale factor.
- (1, 1) becomes (3, 3).
- (3, 1) becomes (9, 3).
- (1, 4) becomes (3, 12). Each side of the image is three times the corresponding side of the original, and the shape is similar to the original.
Describe what happens to a shape when it is enlarged by scale factor minus 2 about a given centre.
Show the worked answer
- The magnitude of the scale factor is 2, so every length in the image is twice the corresponding length in the object.
- The negative sign means the image is on the opposite side of the centre of enlargement from the object.
- The image is therefore inverted, appearing rotated by 180 degrees relative to the object.
- The image is still mathematically similar to the object, since all angles are unchanged and all lengths are in the same ratio.
Common mistakes in this topic
- Omitting the centre when describing a rotation or enlargement.
- Describing a single transformation as a combination of two.
- Giving a translation in words rather than as a column vector.
- Treating a negative scale factor as a fraction.
- Naming a mirror line without its equation.
Exam tips
- Learn the required information for each transformation as a four item checklist and run through it before writing.
- For a rotation, use tracing paper to find the centre by trial if it is not obvious.
- For an enlargement, draw rays through corresponding points. They meet at the centre.
- Column vectors: top is right and left, bottom is up and down.
- If the question says describe fully, expect one mark per piece of required information.
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Transformations FAQs
What information is needed to describe each transformation?
A reflection needs the equation of the mirror line. A rotation needs the centre, the angle and the direction. A translation needs a column vector. An enlargement needs the scale factor and the centre. Cambridge awards a mark for each required piece.
What does a negative scale factor do?
The image is placed on the opposite side of the centre of enlargement and appears inverted, as though rotated 180 degrees. The size is determined by the magnitude of the scale factor, so minus 2 doubles every length rather than halving it.
How do I find the centre of an enlargement?
Draw straight lines through each pair of corresponding points on the object and the image, extending them as needed. All of those rays meet at a single point, and that point is the centre of enlargement.
Why do I lose marks for describing a rotation as two transformations?
When a question asks for a single transformation, the answer must be one transformation completely described. Splitting it into a reflection followed by a translation, for example, does not answer the question as asked and typically scores nothing.
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Written to the published Cambridge IGCSE Mathematics (0580) syllabus. Check your school entry code and syllabus year, because Core and Extended candidates are assessed on different content. Last reviewed 2026-08-12.