# Notes on Affine Transformations

October 15, 2019Previously: Notes on Linear Transformations

## Affine transformations

So far you have used a matrix to perform transformations on a vector, but you cannot use such transforms to *translate* objects, and there's no such way to do it with a 2x2 matrix.

We can use a clever trick to get a single matrix muiltiplication to do both operations together. The idea is simple: represent the posint by a 4d vector and use 3x3 matrices of the form:

m_{11} |
m_{12} |
x_{t} |

m_{21} |
m_{22} |
y_{t} |

This single matrix implements a linear transformation followed by a translation, and this kind of transformation is an *affine transformation*.