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Geometry Transformations

# Transformations and Isometries

A transformation is a process which changes the position (and possibly the size and orientation) of a shape. There are four types of transformations: reflection, rotation, translation and enlargement.

Translation (also known as Slide) moves a shape by sliding it up, down, sideways or diagonally, without turning it or making it bigger or smaller.

Point A has been translated to A'' by moving 8 squared to the right and then 4 squares up. This translation is written as a vector $\fs2A=\left(\begin{matrix}8\\4\end{matrix}\right)$

Reflection (also known as Flip) in a line produces a mirror image in which corresponding points on the original shape and the mirror image are always the same distance from the mirror line.

Rotation (also known as Turn) turns a shape through a clockwise or anti-clockwise angle about a fixed point known as the Centre of Rotation. All lines in the shape rotate through the same angle. Rotation, (just like reflection) changes the orientation and position of the shape, but everything else stays the same.

Enlargement (also known as Dilation) is a transformation. However, it is different from reflection, rotation and translation because it changes the size of an object.

Some of these transformations on an object give a image whose dimensions are different from that of the object. Others produce an image whose dimensions are the same as those of the object. In other words the object and the image are invariant.

Transformations which leave the dimensions of the object and its image unchanged are called isometric transformations. Examples of isometrics are reflection, rotation and translation. Transformations which do alter the dimension of the object when they act on them are called non-isometric transformation Examples are the enlargement.