A translation moves every point by the same column vector. The top component changes x and the bottom changes y: (x,y) to (x+a,y+b). Shape, size and orientation are preserved. Example Translation by 3 -2 sends P(1,3) to P (4,1). Subtract the original coordinates from the image coordinates to recover the vector. A complete description gives the word translation and its vector. “Three right” is incomplete if there is also vertical movement.

A translation moves every point by the same column vector. The top component changes x and the bottom changes y: \((x,y)\mapsto(x+a,y+b)\). Shape, size and orientation are preserved.

Translation by \(\begin{pmatrix}3\\-2\end{pmatrix}\) sends \(P(1,3)\) to \(P\prime(4,1)\). Subtract the original coordinates from the image coordinates to recover the vector.

A complete description gives the word translation and its vector. “Three right” is incomplete if there is also vertical movement.

Plane Transformations

Cambridge IGCSE Mathematics 0580. Initial catalogue covers the assessed demands of February/March 2026 Paper 22; further Core and Extended mappings require paper-level scope review.

Translation as one displacement

Translation as one displacement