Congruency, Enlargement and Combined Transformations · Form 5
Congruency, Enlargement and Combined Transformations: Practice Questions
Original SPM-style practice questions for Congruency, Enlargement and Combined Transformations, each with full worked solutions, Paper 1 multiple-choice and Paper 2 structured.
Original practice questions for Congruency, Enlargement and Combined Transformations, in the style of Mathematics Paper 1 (Objective) and Mathematics Paper 2 (Subjective). Each answer is worked so you can check your method, not just the result.
Multiple-choice (Paper 1 style)
Question 1
Two triangles are congruent if they have the same
- A. shape only
- B. size only
- C. shape and size
- D. area only
Question 2
An object of area 12 cm² is enlarged by scale factor 3. The area of the image is
- A. 36 cm²
- B. 72 cm²
- C. 108 cm²
- D. 144 cm²
Question 3
Under an enlargement, a line of length 4 cm becomes 10 cm. The scale factor is
- A. 2
- B. 2.5
- C. 3
- D. 4
Question 4
Point P(2, 3) is enlarged with centre the origin and scale factor 2. The image P' is
- A. (4, 6)
- B. (2, 6)
- C. (4, 3)
- D. (6, 9)
Question 5
The area of an image is 4 times the area of the object under an enlargement. The scale factor is
- A. 1
- B. 2
- C. 4
- D. 8
Question 6
An enlargement has centre O(0, 0) and scale factor ½. A square of area 48 cm² has an image of area
- A. 6 cm²
- B. 12 cm²
- C. 24 cm²
- D. 96 cm²
Question 7
Point P(2, −3) is rotated 180° about the origin. The image is
- A. (−2, 3)
- B. (−2, −3)
- C. (2, 3)
- D. (3, −2)
Question 8
An enlargement has centre O and scale factor −2. If OA = 3 cm, then OA' (to the image A') is
- A. 6 cm, same side of O
- B. 6 cm, opposite side of O
- C. 1.5 cm, opposite side of O
- D. 3 cm, same side of O
Question 9
Two successive reflections in the parallel lines x = 1 and x = 4 are equivalent to a single
- A. rotation
- B. translation
- C. enlargement
- D. reflection
Question 10
A triangle of area 5 cm² has an image of area 45 cm² under an enlargement. The scale factor is
- A. 3
- B. 6
- C. 9
- D. 15
Structured (Paper 2 style)
Question 1 (6 marks)
Triangle ABC has vertices A(1, 2), B(3, 2) and C(3, 5). An enlargement has centre the origin O(0, 0) and scale factor 2.
(a) Find the coordinates of the images A', B' and C'. (b) Find the area of triangle ABC.
(c) Hence find the area of the image triangle A'B'C', using the relationship between areas.
- (a) With centre O, multiply each coordinate by k = 2.
- A' = (1×2, 2×2) = (2, 4).
- B' = (3×2, 2×2) = (6, 4).
- C' = (3×2, 5×2) = (6, 10).
- (b) AB is horizontal of length 3 − 1 = 2; BC is vertical of length 5 − 2 = 3; the right angle is at B.
- Area of ABC = ½ × base × height = ½ × 2 × 3 = 3 cm².
- (c) Area of image = k² × area of object = 2² × 3 = 4 × 3 = 12 cm².
Question 2 (5 marks)
An enlargement has centre C(2, 1) and scale factor 3. (a) Find the image P' of the point P(4, 3).
(b) A polygon has area 8 cm². Find the area of its image under this enlargement.
- (a) Image = C + k(P − C), applied to each coordinate.
- x' = 2 + 3(4 − 2) = 2 + 3(2) = 2 + 6 = 8.
- y' = 1 + 3(3 − 1) = 1 + 3(2) = 1 + 6 = 7.
- So P' = (8, 7).
- (b) Area of image = k² × area of object = 3² × 8 = 9 × 8 = 72 cm².
Question 3 (6 marks)
Transformation V is a reflection in the y-axis. Transformation W is a translation of (4, 0), meaning 4 units to the right.
(a) Point A(2, 5) undergoes V followed by W. Find the coordinates of the final image.
(b) A second point B(−3, 1) undergoes W followed by V. Find the coordinates of its final image.
(Note the order of the two combined transformations differs in parts (a) and (b).)
- (a) Apply V first: reflection in y-axis maps (x, y) to (−x, y), so A(2, 5) → (−2, 5).
- Then apply W: add 4 to the x-coordinate, (−2, 5) → (−2 + 4, 5) = (2, 5).
- Final image of A is (2, 5).
- (b) Apply W first: B(−3, 1) → (−3 + 4, 1) = (1, 1).
- Then apply V: reflection in y-axis, (1, 1) → (−1, 1).
- Final image of B is (−1, 1).
Question 4 (5 marks)
An enlargement has centre the origin O(0, 0) and scale factor −2. (a) Find the image of the point P(3, 1).
(b) A shape has area 6 cm². Find the area of its image.
(c) State one way the image differs in position from an enlargement with scale factor +2.
- (a) With centre O, multiply each coordinate by k = −2.
- P' = (−2 × 3, −2 × 1) = (−6, −2).
- (b) Area depends on k²: area of image = k² × area = (−2)² × 6 = 4 × 6 = 24 cm².
- (c) Because k is negative, the image lies on the opposite side of the centre O from the object (and is inverted through O), whereas with k = +2 it stays on the same side.
Source:SPM: Format Pentaksiran mulai 2021, Matematik (1449)
Frequently asked questions
What's in this practice set for congruency, enlargement and combined transformations?
It has Paper 1 questions testing whether shapes are congruent or identifying enlargement scale factors, plus Paper 2 structured questions on drawing images under combined transformations. All questions are original practice for this site, not taken from real SPM papers.
Why try the question myself before checking the worked solution?
Sketching the transformation yourself first, even if the final shape looks off, shows exactly where your understanding of the transformation sequence went wrong. Reading the solution before attempting removes that useful struggle and makes the topic feel easier than it is in the exam.
What mistake is common with combined transformations?
Students often apply the two transformations in the wrong order, which changes the final image. Always perform the transformation closer to the object first, label each image clearly as it's formed, and check your scale factor and centre of enlargement against the worked solution.