Yeah, I thought of that (and probably should have listed it in my original post), but I still don't know how to integrate it into this solution. Here's some further thoughts:

Let

= the positively sloping line and

be the negatively sloping line.

Let

pass through the points,

and

where

.

Since

is even, this means that

passes through

and

.

As you point out, the slopes are negative reciprocals of each other, by definition.

Then, there are a couple of things that I think are true, but I don't know just how to prove them. First

and

. I say this because, in order to be tangent to an even function, the only way that I can see two perpendicular lines meeting at the y-axis would be if they both had symmetrical x-coordinates (e.g. (5, 0) and (-5, 0)).

If that is true, this final one might be the key to the whole thing. If the slope is 1 or -1, and the lines intersect at the y-axis, then doesn't

have to equal

?

Am I on the right track? Making this to complicated? Any help is appreciated.

Thanks again.