Verify that the following mappings are isometries on R^2
Reflection Through the Origin
Qualities of a metric:
d(x,y) = d(y,x)
d(x,x) = 0
d(x,y) = 0 <=> x = y
d(x,y) =< d(x,z) +d(z,y)
The Attempt at a Solution
As a metric hasn't been specified, I have been trying to prove this for a general metric using just the intrinsic qualities. I haven't had much luck, though.
I know that all three are straightforward to prove in Euclidean Space, which gives a metric. But is there a simple proof for a general metric?
I may have misunderstood the meaning of Verify, but would nevertheless like a proof if there is one.