Congruency, Enlargement and Combined Transformations · Form 5
Congruency, Enlargement and Combined Transformations: Paper 2 Answering Guide
How Congruency, Enlargement and Combined Transformations appears in Mathematics Paper 2 (Subjective), and how to lay out your working so you earn every method mark.
How it is examined
Paper 2 gives shapes on a grid and asks you to describe a transformation fully, find an image, or work out an area using the scale factor. Full description marks are strict, a rotation needs centre, angle and direction, so precision is everything here.
Showing your working
Mathematics Paper 2 (Subjective) is worth 100 marks and gives marks for the steps, not only the answer. Write each line clearly: state the formula or rule, substitute the numbers, then simplify.
If the question carries units, carry them through to the final line.
The question
Question (Paper 2 style, worth 6 marks). On a square grid, triangle P has vertices A(2, 1), B(2, 3) and D(3, 1), and its image P' has vertices A'(3, 1), B'(3, 5) and D'(5, 1).
(a) Describe fully the single transformation that maps P onto P'. (b) Given that the area of triangle P is 1 unit², find the area of triangle P'.
Mark-earning layout, line by line
- State the type: the image is the same shape but larger, so the transformation is an enlargement.
- Find the centre by joining corresponding points and extending. Line A A' is y = 1. Line B B' passes through (2, 3) and (3, 5): gradient 2, equation y = 2x − 1. They meet where 1 = 2x − 1, so x = 1, giving centre (1, 1).
- Find the scale factor: the distance of A from the centre is 1 unit and of A' from the centre is 2 units, so k = 2 ÷ 1 = 2.
- Write the full description for part (a): enlargement, centre (1, 1), scale factor 2.
- For part (b), state the rule: area of image = k² × area of object.
- Substitute and simplify: area of P' = 2² × 1 = 4 × 1 = 4 unit².
Source:SPM: Format Pentaksiran mulai 2021, Matematik (1449)
Frequently asked questions
Do I have to draw the construction lines to find the centre, or can I just write the coordinates?
Show the construction. Joining two pairs of corresponding points and extending them earns the method mark and proves your centre; a bare coordinate can be marked wrong with no way back.
On a grid you may draw the rays lightly with a ruler, then read the intersection, that is enough working.
How are the marks usually split in a 'describe fully' enlargement?
Typically one mark for naming the transformation as an enlargement, one for the correct centre, and one for the correct scale factor with its sign. Miss any single part and that mark is gone.
So always write all three, enlargement, centre (…), scale factor …, even when one feels obvious.
For the area part, can I just count grid squares instead of using k²?
You can check by counting, but show the k² method for the marks. The examiner is testing whether you know area scales by the square of the scale factor, so write area of image = k² × area of object and substitute.
Use the square count only to confirm your answer looks right.