Translations

A translation is a type of transformation that moves a shape from one position to another without rotating, resizing, or flipping it. In a translation, every point of the shape moves the same distance in the same direction. Translations can be described using vectors.

Vector Notation

A vector describes the movement in a translation and is written in the form:

\[ \begin{pmatrix} right \\ left \end{pmatrix} \]

Translating a Shape

If the vector to translate a shape is:

\[ \begin{pmatrix} 3 \\ -2 \end{pmatrix} \]

then:

• Move each vertex (corner) on the shape 3 units to the right (positive horizontal movement).
• Move each vertex (corner) on the shape 2 units down (negative vertical movement).