Congruency, Enlargement and Combined Transformations · 5.2.3
Finding the image and object of an enlargement
This standard requires students to calculate the coordinates or dimensions of an image given the object, centre and scale factor of an enlargement, and conversely to find the object given the image, applying the relationship between object, centre, and scale factor.
The official learning standard (5.2.3)
“Determine the image and object of an enlargement.”
What it means
This standard requires students to calculate the coordinates or dimensions of an image given the object, centre and scale factor of an enlargement, and conversely to find the object given the image, applying the relationship between object, centre, and scale factor.
How it is examined
Paper 1 questions typically ask students to calculate a single image or object coordinate given the enlargement's centre and scale factor. Paper 2 questions require finding full sets of coordinates or lengths on a grid, sometimes combined with area or coordinate geometry.
Worked example
Point A has coordinates (2,3). Under an enlargement with centre O(0,0) and scale factor 3, find the coordinates of the image, A'.
- Use the enlargement formula: image = centre + k × (object − centre), with centre O(0,0) and scale factor k = 3.
- Find object − centre: (2 − 0, 3 − 0) = (2, 3).
- Multiply by the scale factor: 3 × (2, 3) = (6, 9).
- Add the centre coordinates: (0, 0) + (6, 9) = (6, 9).
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
How do I find the object if I'm given the image and the enlargement?
Rearrange the formula: object = centre + (1/k) × (image − centre). This applies the inverse enlargement, using scale factor 1/k, to the image point to recover the original object coordinates.
What happens if the centre of enlargement is not the origin?
You must subtract the centre's coordinates first, multiply by the scale factor, then add the centre's coordinates back, the formula image = centre + k(object − centre) works for any centre, not only the origin.
Does an enlargement change the shape of the object?
No, enlargement only changes size (and sometimes orientation, if k is negative), never the shape. The image is always similar to the object, with equal angles and sides in the same ratio.