$1000M for 9 miles of light rail isn't completely crazy (expensive, but believable). The average cost in the UK is £25M/mile ($40M), but Edinburgh's cost £100M/mile ($156M). A lot of the cost is moving whatever's buried under the road out of the way, to allow future repairs without disrupting the tram.
It's a lot cheaper to build something outside a city on worthless land, whether rail or road.
The 2009 cost per mile for building a 2+2 road in the UK was £13M, for a basic two-lane road £8M. Are you sure your final figure is correct?
(NB the British rail costs will include all appropriate safety systems. This article is interesting. It's over 8 years since a passenger on a train died in Britain, though some have died falling down stairs/escalators, off platforms etc.)