While your solution was not dead on, it did lead me to transformation matrices, and essentially the system works like this:
First, the angular distance between the point to be reflected and the line over which it is to be reflected must be determined (this is assuming the line's y-intercept lies at 0).
point A = (0, 1)
line Q = y = x
The difference between the angular measurements of these two objects is 45 degrees.
Doubling this, we get the rotational difference (and thus the rotational difference): 90 degrees.
Next a transformational matrix is used (see included picture) to determine the new x and y coordinates of the point (x' and y').
I hope this helps everyone out there (doubtfully) who needs this kind of information.
