1
$\begingroup$

enter image description here

In the picture above two sets of parallel lines are given: $l, m$ and $p, q$. when can we say these pairs are the same? If the distance or altitude are same then can we say they are equal?

$\endgroup$
  • $\begingroup$ One line from each pair is same and the signed distance of that line from the remaining two are same. Or the two lines of in one pair has the same equations as the two lines in other pair. $\endgroup$ – Dhruv Kohli - expiTTp1z0 Jun 19 '17 at 4:32
1
$\begingroup$

I think that they will be equal if they represent same set of equations. For instance if the set of two lines l and m have equations $2x+3y=8$ and $2x+3y=6$ while the p and q have equations $2x+3y=8$ and $2x+3y=6$ (in any order) then these two sets of lines will be equal.

$\endgroup$
1
$\begingroup$

It depends on your definition of equivalence class. You can define two lines equivalent if they are parallel. I don't know if this is what you meant.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.