i just really need help getting started showing that the reflection of (x,y) thru the line y=x is the point with coord. (y,x).
p.s. of course this is due tomorrow morning --- however i dont think i will score very well on this one (i wish i could just figure out how to prove stuff, any help there would also be appreciated...) ;)
Reflection of a function through the line y(x)=x amounts to finding the inverse of the function in question. You do that by (if it's a function y of x which usually comes already solved for y) solving the equation for x (so you'll end up with x=y^2+3*y-1 or whatever). Then, you plug in a y value and do the computations to see which x comes out. So, for the point (x,y), which means originally you'd plug in x to get y, now in the inverse function you'll be plugging in the result, y and you know by the equation x=y that you'll get x back, so the new reflected point is (y,x).