Translation

To perform translation, you want to leave the x,y components alone while adding the translation factors to x,y. This matrix will do the job:

    |1  0  0 |
Mt =|0  1  0 |
    |dx dy 0 |

Example:

p = [x y 1]

                      |1  0  0 |
p' = p*Mt = [x y 1] * |0  1  0 | = [(x+1*dx) (y+1*dy) 1]
                      |dx dy 1 |

And if you pull out the first two elements, you get

x' = x+dx
y' = y+dy

This is exactly what you wanted.