This is because the formula for the hyperbolic distance between two points A and B is derived by assuming that units have been adjusted so that C=1 (this is not stated very clearly in Penrose's book and of course the derivations of the formulae are not presented either). So this means that the distances given by the formula are all effectively multiplied by

. In order therefore to get back to distances measured in the previous units we have to divide by

or multiply by

.

I hope this is clear, if not please let me know.

To summarise: lengths were multiplied by an appropriate

so that C could be 1 and so to get distances back to the original units we must divide by

.