The reason behind the name "Orthogonal transformation". An orthogonal transformation is a linear transformation such that $(Tx,Ty)=(x,y)$. 
Orthogonality is suggestive of perpendicularity. What might have been the reason for naming a distance preserving linear transformation on a vector space "orthogonal"?
Thanks!

I think it's due to the fact that, in a finite dimensional vector space, the columns of the associated matrix of the transformation are mutually orthogonal.
They don't just preserve distance, they also preserve inner product. In more familiar examples, you can think of this as preserving the angle between two vectors. 
