Image = centre + k × (object − centre). Scale factor k stretches distances from the centre.
Key formulas
Positive k
k=2 from origin doubles coordinates. From another centre, use the vector form so the centre stays fixed.
Example
Centre (0,0), k=3, point (2,−1) → (6,−3).
Negative k
k=−1 is enlargement with rotation 180° about the centre — rays go through C and continue the same distance beyond.
Worked example
Worked example
Problem. Enlarge point (2, −1) from the origin with scale factor 3.
Solution. Image = 3(2, −1) = (6, −3).
Area
Areas scale by k².
Review quiz
Centre O, k=4, point (5,−6). Image is:
Practice questions
- Centre O, k=½, point (8,2). Find the image.
- Centre (1,1), k=2, point (1,4). Find the image.
Study notes
Is enlargement a rigid motion?
No — lengths change unless |k|=1.