To enlarge a plane figure by positive factor k about centre O, put each image vertex on the ray from O through its original vertex, at k times the distance. Join the image vertices in the same order. Angles remain unchanged. Example If OA=3 cm and OB=5 cm, an enlargement of factor 2 puts A' and B' at 6 cm and 10 cm from O. A reduction of factor 12 puts them at 1.5 cm and 2.5 cm. A map scale 1:25,000 means 1 cm represents 25 000 cm, or 250 m. A 6 cm road represents 1.5 km. For areas, 1 cm2 represents 2502=62,500 m2; a 4 cm² lake represents 250,000 m2=0.25 km2. Scale has no units when both lengths use the same unit. Convert units carefully before squaring; do not use the length scale directly for an area.

To enlarge a plane figure by positive factor \(k\) about centre \(O\), put each image vertex on the ray from \(O\) through its original vertex, at \(k\) times the distance. Join the image vertices in the same order. Angles remain unchanged.

If \(OA=3\text{ cm}\) and \(OB=5\text{ cm}\), an enlargement of factor 2 puts \(A'\) and \(B'\) at 6 cm and 10 cm from \(O\). A reduction of factor \(\dfrac12\) puts them at 1.5 cm and 2.5 cm.

A map scale \(1:25\,000\) means 1 cm represents 25 000 cm, or 250 m. A 6 cm road represents 1.5 km. For areas, \(1\text{ cm}^2\) represents \(250^2=62\,500\text{ m}^2\); a 4 cm² lake represents \(250\,000\text{ m}^2=0.25\text{ km}^2\).

Scale has no units when both lengths use the same unit. Convert units carefully before squaring; do not use the length scale directly for an area.

Enlargements and map scales

Enlargements and map scales