Im curious as to why we do not need to specify return "false" or "true" in this example?

Math is allowed, what you are getting is:
"Math::DomainError (Numerical argument is out of domain - "sqrt")"
you could use 'raise' to attend it or use logical expression to ensure the positive range of the number before use Math::sqrt

if cartesian plane uses x,y , why use e,n? Makes it less clear...

Thanks for mentioning. I am new on this platform and didn't know the purpose of spoiler flag. Now I knnow. Thanks :)

Use spoiler flag, please.

You get this error when you pass a negative value to Math.sqrt. You can't pass negative to it.

i agree, for example 1e16+1 returns true when it shouldn't

It doesn't reinvent the wheel which is what makes it a good solution.

If the kata wanted us not to use Matrix#det, it should have locked that method.

hmm.. i kept getting sqrt error. not sure why. thought Math.sqrt isn't supported here.

isnt sort supposed to be time consuming? instead of just a single pass you are doing an nlogn operation just for sorting

sure using matrix... this is cheating

this makes the most sense.