Transformations
Cambridge IGCSE Mathematics (0580) · Unit 7: Transformations and vectors · 9 flashcards
Transformations is topic 7.1 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 7 — Transformations and vectors , alongside Vectors. In one line: The column vector represents a translation. The top number (3) indicates a shift of 3 units in the positive x-direction (right), and the bottom number (-2) indicates a shift of 2 units in the negative y-direction (down).
This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator.
The deck below contains 9 flashcards — 4 definitions, 2 key concepts and 1 application card — covering the precise wording mark schemes reward. Use the 4 definition cards to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.
Describe the transformation represented by the column vector (3, -2)
The column vector represents a translation. The top number (3) indicates a shift of 3 units in the positive x-direction (right), and the bottom number (-2) indicates a shift of 2 units in the negative y-direction (down).
Questions this Transformations deck will help you answer
- › What single transformation maps object A onto image B, given that A and B are congruent?
- › Describe a rotation of 90° clockwise about the origin.
- › Shape A is reflected in the line x = 1 to create shape B. Shape B is then reflected in the line x = 3 to create shape C. Describe the single transformation that maps A onto C.
What single transformation maps object A onto image B, given that A and B are congruent?
A single transformation will map one congruent shape to another if it is a translation, reflection, or rotation. Consider the orientation and position to determine the correct transformation.
Describe the transformation represented by the column vector (3, -2).
The column vector represents a translation. The top number (3) indicates a shift of 3 units in the positive x-direction (right), and the bottom number (-2) indicates a shift of 2 units in the negative y-direction (down).
A shape is reflected in the line y = x. What are the coordinates of the image point of (2, 5)?
When reflecting in the line y = x, the x and y coordinates are swapped. Therefore, the image of (2, 5) is (5, 2).
Define 'enlargement' and explain what two pieces of information are needed to fully describe an enlargement.
An enlargement changes the size of an object by a scale factor. To describe it fully, you need to state the scale factor and the centre of enlargement.
Object A is enlarged with a scale factor of 2, centre (0,0), to create image B. If point P on A is (1,3), what are the coordinates of the corresponding point P' on B?
Multiply the coordinates of the original point by the scale factor. P'(2*1, 2*3) = P'(2, 6).
What does it mean for two shapes to be 'congruent'?
Congruent shapes are identical; they have the same size and shape. One can be mapped onto the other by a translation, rotation, or reflection.
What does it mean for two shapes to be 'similar'?
Similar shapes have the same shape but can be different sizes. One can be mapped onto the other by an enlargement (or reduction) along with a possible translation, rotation, or reflection.
Describe a rotation of 90° clockwise about the origin.
A rotation requires three pieces of information: the angle of rotation (90°), the direction of rotation (clockwise), and the centre of rotation (the origin).
Shape A is reflected in the line x = 1 to create shape B. Shape B is then reflected in the line x = 3 to create shape C. Describe the single transformation that maps A onto C.
Two successive reflections in parallel lines is equivalent to a translation. The distance moved will be twice the distance between the parallel mirror lines. So this is a translation of (4,0).
Key Questions: Transformations
Describe the transformation represented by the column vector (3, -2).
The column vector represents a translation. The top number (3) indicates a shift of 3 units in the positive x-direction (right), and the bottom number (-2) indicates a shift of 2 units in the negative y-direction (down).
Define 'enlargement' and explain what two pieces of information are needed to fully describe an enlargement.
An enlargement changes the size of an object by a scale factor. To describe it fully, you need to state the scale factor and the centre of enlargement.
What does it mean for two shapes to be 'congruent'?
Congruent shapes are identical; they have the same size and shape. One can be mapped onto the other by a translation, rotation, or reflection.
What does it mean for two shapes to be 'similar'?
Similar shapes have the same shape but can be different sizes. One can be mapped onto the other by an enlargement (or reduction) along with a possible translation, rotation, or reflection.
Tips to avoid common mistakes in Transformations
- ● For reflections, rotations, and translations, the image shape must match the object exactly; for enlargements, specify the centre of enlargement carefully.
- ● For each transformation, state its TYPE and all parameters: centre point (if relevant), plus either scale factor or rotation angle.
- ● Always read the question carefully to determine if a single transformation is required.
- ● If the figure doubles in size, name the single transformation properly: 'Enlargement, scale factor 2, centre of enlargement (x, y)'.
- ● Focus solely on the single transformation requested in the question.
More topics in Unit 7 — Transformations and vectors
Transformations sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.
Cambridge syllabus keywords to use in your answers
These are the official Cambridge 0580 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.
Key terms covered in this Transformations deck
Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.
Related Mathematics guides
Long-read articles that go beyond the deck — cover the whole subject's common mistakes, high-yield content and revision pacing.
How to study this Transformations deck
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