into 
:
This motion takes 
into
and the line through and into the line through and 
. The edgepoints of this new line are the real multiples of 
with modulus 
, i.e. they are 
and 
. Then 
, so 
.
We repeat the earlier example, but now use the fact that Poincaré motions don't change distances.
| Apply a Poincaré motion taking one of the points, say, into :
This motion takes and the line through |
|