Congruency, Enlargement and Combined Transformations · 5.2.2
Describing enlargement transformations
Students learn that enlargement is the transformation that produces an image similar to the object, then describe an enlargement completely by stating its centre and scale factor, using diagrams, coordinates, or ratio notation to represent the transformation clearly and precisely.
The official learning standard (5.2.2)
“Make a connection between similarity and enlargement, hence describe enlargement using various representations.”
What it means
Students learn that enlargement is the transformation that produces an image similar to the object, then describe an enlargement completely by stating its centre and scale factor, using diagrams, coordinates, or ratio notation to represent the transformation clearly and precisely.
How it is examined
Paper 1 often asks students to state the scale factor or centre of enlargement directly from a diagram. Paper 2 requires fuller descriptions, identifying both centre and scale factor from an object and its image plotted on a grid or Cartesian plane.
Worked example
Triangle ABC has vertices A(1,1), B(3,1) and C(1,3). Under an enlargement, its image is triangle A'B'C' with vertices A'(2,2), B'(6,2) and C'(2,6).
Describe the enlargement completely.
- Compare corresponding coordinates: A(1,1)→A'(2,2), B(3,1)→B'(6,2), C(1,3)→C'(2,6).
- Notice each image coordinate is exactly double the corresponding object coordinate (e.g. A' = 2×A), so the centre of enlargement must be the origin, O(0,0).
- Calculate the scale factor using the ratio of a corresponding distance: OA' ÷ OA = 2, confirming the scale factor k = 2.
- State the description: enlargement with centre O(0,0) and scale factor 2.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
What two pieces of information fully describe an enlargement?
The centre of enlargement (a fixed point) and the scale factor (how many times bigger or smaller the image is compared to the object). Both must be stated together for a complete description of the transformation.
Can the scale factor be negative or a fraction?
Yes. A fraction between 0 and 1 gives a smaller image (a reduction), while a negative scale factor places the image on the opposite side of the centre, inverted relative to the object.
Why is the image of an enlargement always similar to the object?
Because every length is multiplied by the same scale factor while all angles stay unchanged, so corresponding angles remain equal and corresponding sides remain in a constant ratio, exactly the definition of similarity.