1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Rays, points and line segments

  1. Feb 17, 2014 #1
    1. The problem statement, all variables and given/known data

    Let A, B and D be points. If ##D\notin \vec{AB}## in a metric geometry, prove that ##\vec{AD}\cap\vec{AB} = \{A\}.##


    2. Relevant definitions

    Ray: If A and B are distinct points then the ray from A toward B is the set ##\vec{AB} = \overline{AB}
    \cup \{ C \in P \ | \ A-B-C\},## where ##A-B-C## means B is between A and C.

    Line segment: If A and B are distinct points in a metric geometry then the line segment from A to B is the set ##\overline{AB} = \{C\in P\ | \ A-C-B \ \text{or} \ C=A \ \text{or} \ C = B\}.##

    3. The attempt at a solution

    I am not sure how to go about proving this.

    If I let ##Z## be a point where ##Z\in\vec{AD}## then ##Z\notin\vec{AB}## since ##Z## was arbitrary then there are no points in ##\vec{AD}## that lie in ##\vec{AB}##. So ##A## is the only point in ##\vec{AD}\cap\vec{AB}##.
     
  2. jcsd
  3. Feb 18, 2014 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi Lee33! :smile:
    Haven't you just assumed exactly what you have to prove? :confused:

    And don't say "Z is arbitrary", it's almost meaningless … say "if Z ≠ A then A – Z – D"

    (However, I don't understand the question … why can't D be along the extended line AB, the other side of B ??)
     
  4. Feb 18, 2014 #3
    Well the question is asking if the point D is not in the ray ##\vec{AB}## then I must prove that ##\vec{AB}\cap\vec{AD}## equals the set {A}.
     
    Last edited: Feb 18, 2014
  5. Feb 18, 2014 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    but there's no C in the question :confused:
     
  6. Feb 18, 2014 #5
    Opps. I meant A instead of C. I have edited the post. Sorry about that.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Rays, points and line segments
  1. Line Segment (Replies: 6)

Loading...