The group of matrices of the form below with ad-bc≠0 forms the affine group of the plane.
The linear action of such matrices preserves the plane z=1 in R3. We identify this plane with the (x,y)-plane in the obvious way. So, the matrix acts according to the following equation:
Multiplication by M converts from the new coordinate system to the old coordinate system.
In the following example, we reflect the text "Hello!" in the red line, y=0.
01: <svg version="1.1" baseProfile="full" 02: xmlns="http://www.w3.org/2000/svg" 03: width="300px" height="110px" viewBox="0 -55 300 110" 04: font-family="Times, serif" font-size="50px"> 05: 06: <text x="5" y="-5">Hello!</text> 07: <line x1="0" y1="0" x2="300" y2="0" stroke="red" stroke-width="1px"/> 08: <text x="5" y="-5" transform="matrix(1,0,0,-1,0,0)" fill="blue">Hello!</text> 09: 10: </svg> 11: