A transformation is a change in position, size or shape of an object. Transformation includes:
- Reflection
- Rotation
- Enlargement
- Translation
- Shear
Matrices can be used to transformation an object by multiplying vertices of an object on a Cartesian plane with a 2 x 2 matrix
Reflection on line x=0 (Y-axis)
The matrix that can map objects on this transformation is

Reflection on Y=0 (X-axis)
multiply the object with

Reflection on the line y=x
multiply the object vertices by:

Reflection on the line y= -x
multiply the object vertices by:

positive Quarter turn about the origin
positive turn is turning anticlockwise. Multiply the object vertices by

Half turn about the origin
Multiply the object vertices by:

Positive three quarter turn about the origin
This is same as rotating 270o anticlockwise. Multiply the object vertices by:

An Enlargement from center with a scale factor k
Multiply the object vertices by:


