Congruency, Enlargement and Combined Transformations · 5.2.5
Solving enlargement problems
This standard requires students to apply the concepts of centre, scale factor, image and object coordinates, and the area relationship together to solve multi-step problems involving enlargement, including practical situations such as maps, photographs, scale models, and technical drawings carefully.
The official learning standard (5.2.5)
“Solve problems involving enlargement.”
What it means
This standard requires students to apply the concepts of centre, scale factor, image and object coordinates, and the area relationship together to solve multi-step problems involving enlargement, including practical situations such as maps, photographs, scale models, and technical drawings carefully.
How it is examined
Paper 2 mainly features multi-part structured questions combining finding the centre or scale factor, calculating image or object coordinates, and determining the area of an enlarged shape, sometimes set in real-world contexts like maps, photographs, or scale models.
Worked example
A rectangular photo measuring 4 cm by 6 cm is enlarged with a scale factor of 3 to make a poster. Find (a) the dimensions of the poster and (b) the area of the poster.
- Since the scale factor is k = 3, multiply each side length of the photo by 3: 4 × 3 = 12 cm and 6 × 3 = 18 cm, giving the poster's dimensions.
- Calculate the area of the poster directly: Area = 12 × 18 = 216 cm².
- Verify using the area relationship: Area of object = 4 × 6 = 24 cm²; Area of image = k² × 24 = 9 × 24 = 216 cm², which matches.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
What's the general strategy for enlargement problems in Paper 2?
Identify what is given (object, image, centre, scale factor, or area) and what is asked, then apply the correct formula, image = centre + k(object − centre) for coordinates, or Area of image = k² × Area of object for areas, showing every step clearly.
How do real-life enlargement problems usually appear in SPM?
They often involve maps, photographs, models, or scale drawings, where you calculate actual or scaled lengths and areas using a given scale factor, sometimes requiring unit conversions such as centimetres to metres.
What if the scale factor is unknown but corresponding lengths are given?
Calculate the scale factor first using k = corresponding image length ÷ corresponding object length, then use this k to solve the rest of the problem, including any area calculations required.