Translations Flashcards

A type of transformation that moves a shape without rotating or reflecting it.

A way to describe a translation using a column vector, e.g., \( \begin{pmatrix} a \\ b \end{pmatrix} \), where \(a\) is the horizontal movement and \(b\) is the vertical movement.

The top number in the column vector, which shows how far the shape moves left (negative) or right (positive).

The bottom number in the column vector, which shows how far the shape moves down (negative) or up (positive).

A translation moves the shape to a new position but does not change its size, shape, or orientation.

The vector \( \begin{pmatrix} 3 \\ -2 \end{pmatrix} \) means move 3 units right and 2 units down.

To translate a point, add the vector's horizontal and vertical components to the point's coordinates.

There are no invariant points in a translation because every point on the shape moves.

A translation is fully described by giving the column vector.

Translation moves a shape without changing its size, shape, or orientation, unlike rotation, reflection, or enlargement.