Isometry in the Plane

Isometry in the Plane

TransformationsTakes any point in the plane and maps it to another point.

Iso 1 (image/png)

Iso 2 (image/png)

Caption: : Translation

RotationWhen a point is rotated by a given angle about the centre of rotation.A rotation about the origin through α (anticlockwise) is represented by:

Iso 3 (image/png)

ReflectionWhen a point is reflected in a fixed line.A reflection in the line y=xtanα is represented by:

Iso 4 (image/png)

Linear TransformationA transformation that maps the origin onto itself, e.g. rotations and reflections with centres at the origin.Isometry is the study of linear transformations where the area of the transformed shape = area of the original shape, i.e. the determinant = 1.