How to express an angle of 90 degrees between two lines?

Question

If I would extend two lines $l_1$ and $l_2$ they would intersect with an angle of 90 degrees. How should I write with math terms that there would be a 90 degree angle. I assume $l_1 \perp l_2$ is wrong if they do not intersect (when not extending them).

Is there a possibility to express a 90 degree angle between an extension of $l_1$ and $l_2$? How to express an extension of $l_1$?

Answer 1

Generally lines are thought to go on indefinitely (they don't have endpoints), so the $l_1$ and $l_2$ you are describing should really be called line segments. With that in mind you could say something like:

Let $\ell_1$ and $\ell_2$ be the lines that contain the line segments $l_1$ and $l_2$ respectively. Note that $\ell_1 \perp \ell_2$.

Answer 2

We can recognize by what changes occur in the equation of the line.The product of slopes is -1.

If the lines are in slope intercept form

$$ y= m x + a \,\rightarrow y= -x/m + const $$

If in full intercept form

$$ \frac{x}{a}+ \frac{y}{b} =1 \rightarrow \frac{x}{b} - \frac{y}{a} = const $$

If in polar form

$$ x \cos \alpha + y \sin \alpha = p \, \rightarrow -x \sin \alpha + y \cos \alpha = q $$

etc.