EASD

Four distinct lines lie in a plane, and exactly two of them are parallel. Which of the following could be the number of points where at least two of the lines intersect?

Three
Four
Five

A. I only
B. III only
C. I and II only
D. I and III only
E. I, II, and III


I believe the answer is E but according to collegeboard, it is actually D. However, I can create 4 point of intersection if I place the 2 non parallel lines over the parallel ones in a nonparallel fashion. Can someone help explain?

lolcats4

No, it is not possible to create only 4 intersections. Check to see if you are missing anything. Think of it as a rule: All non-parallel lines MUST intersect. There are no exceptions.

You will always get 5 intersections, unless the intersection of the two non-parallel lines ALSO intersects with one of the parallel lines, in which case you get 3 intersections.

simple1

Only way you can have four points intersecting is if you have 2 pairs of parallel lines. The only choice is 3 and 5.

EASD

mmm! I see it now. Thank you!

patricklin27

yeah that was what i was thinking until i visualed it.


It cant be 4 because the two non parallel lines HAVE to intersect each other.

EASD

^ exactly. I didn't draw the lines out long enough to see them intersect. Haha! How very simple it actually is

Ajjared

this question had me for a second too, until i remembered the lines were in one plane. gotta read the question

Amandeep1

In what setup can we get 3 interceptions if the lines continue forever?

nontraditional

Suppose that the 2 non-parallel lines intersect one another at the same point at which they both intersect one of the parallel lines.