Determine if segment is between two lines

Question

I need to find out, if segment n is on the same side of the point F with segment XY.

All lines and segments are parallel, and length of the segments are same. In the illustration red segment AB is on the left side (of the line that strikes through point F). Blue segment CD is right (out)side given criteria.

How do you determine these two case in GeoGebra or Python?

Special case when segment is on F or E lines should be considered too. I hope this was enough for problem description.

Segment *n* could be `AB` or `CD`. He gave two examples of how segment *n* could be — TuanDT, Dec 16 '16 at 14:18
Maybe this [answer](http://stackoverflow.com/a/1560510/4788274) helps you... — José Sánchez, Dec 16 '16 at 14:19
I think this question could be done fairly easy if you are familiar with basic vector algebra (projection, dot products etc. ....) and hence should be directed to a math page such as `mathoverflow`. Translating the formulae into code should be fairly simple — TuanDT, Dec 16 '16 at 14:21
Yes, n is unnamed segment. And yes, Im always strugling between math and code exchange sites. — MarkokraM, Dec 16 '16 at 14:34

Gribouillis · Answer 1 · 2016-12-16T14:46:57.037

Here is how you could do it

u = (y[1]-y[0], x[0]-x[1])
delta = f[0] * u[0] + f[1] * u[1]
if delta < x[0]*u[0]+x[1]*u[1]:
    delta = -delta
    u = (-u[0], -u[1])
assert a[0] * u[0] + a[1] * u[1] < delta
assert b[0] * u[0] + b[1] * u[1] < delta
assert c[0] * u[0] + c[1] * u[1] > delta
assert d[0] * u[0] + d[1] * u[1] > delta

explanation: vector u is orthogonal to XY. The points that have a given scalar product with u form a line parallel to XY. For F this scalar product is delta. By optionally changing the sign of u, one can have delta greater for F than for X. Now the points which scalar product with u is greater than delta are on a parallel line that is farther from XY than the point F

Edit: sorry for the bugfix

Determine if segment is between two lines

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