Question

.

Answer 1

I think you could set up a proof for this based on coordinate geometry. That would be the first way that comes to my mind.
Pretty much the goal is to set up an arbitrary point (a, b) on one side of the line y=x and find the other point by distance formula and linear equations. That might be more convoluted than what this class calls for maybe?

Answer 2

Oops, I went into one way but realized I was getting into circle equations and solving that business. I think your way may be easier to employ!

Well, the line containing (a,b) and perpendicular to y= x should also contain our reflected point. And the distance from (a,b) to the intersection of those two lines is the determining factor of reflections in most cases. That might make for something! :)

Answer 3

Something to that effect.