Positive, fractional and negative enlargement

For centre C and scale factor k, the image displacement is \(\overrightarrow{CP\prime}=k\overrightarrow{CP}\). A positive k keeps the image on the same ray from C. A negative k puts it on the opposite ray. Lengths multiply by \(|k|\); areas multiply by \(k^2\).

Example

With centre \((1,1)\), factor \(-2\) sends \(P(3,2)\) to \((1,1)-2(2,1)=(-3,-1)\).

The illustration uses centre O and factor −2. A factor between 0 and 1 gives a smaller image; a negative factor does not necessarily do so. To identify an enlargement, extend corresponding point–image lines to find the centre and compare signed displacements.