Another way to think of it is to calculate the unit vector for a given direction and then apply a 90 degree counterclockwise rotation to get the normal vector.
The matrix representation of the general 2D transformation looks like this:
x' = x cos(t) - y sin(t)
y' = x sin(t) + y cos(t)
where (x,y) are the components of the original vector and (x', y') are the transformed components.
If t = 90 degrees, then cos(90) = 0 and sin(90) = 1. Substituting and multiplying it out gives:
x' = -y
y' = +x
Same result as given earlier, but with a little more explanation as to where it comes from.