Results 1 to 6 of 6

Math Help - Collinear Points

  1. #1
    Newbie
    Joined
    Sep 2007
    Posts
    8

    Collinear Points

    Can someone please help. This problem is confusing and I just can't figure it out.

    Definition: Points that lie on the same line are called collinear.
    Not sure if you need a minimum of three points in on a same line to be considered collinear.


    Question

    Five point A-E, NO definite lines drawn. E, D and C appear to be in line, A is below D, B is below C

    Conside points A,B,C,D and E as shown

    1. If two of these points are selected at random, what is the probability that they are collinear?
    2. If three of these points are selected at random, what is the probability that they are collinear?
    3. If four of these points are selected at random, what is the probability that they are collinear?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    Without actually seeing the diagram there is no way to answer parts (b) & (c).
    However, the answer to (a) is 1: any two points determine a line.

    Can you use a PAINT type program to insert the diagram?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2007
    Posts
    23


    Here's the picture. I am a friend of sk8ingkittty and I also tried to figure this out but it seems there is not enough info to do that. Thanks for your help.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    O.K. then.
    I thought that might be the diagram. I assume that eab are meant to be in a line.

    The combination of five points taken three at a time, \left( {\begin{array}{c}<br />
   5  \\<br />
   3  \\<br />
\end{array}} \right) = 10.
    From the diagram there are only two subsets of three that are collinear. So what is the answer to (b)?

    \left( {\begin{array}{c}<br />
   5  \\<br />
   4  \\<br />
\end{array}} \right) = 5, how many subsets of four are collinear? So what is the answer to (C)?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,683
    Thanks
    614
    Hello, sk8ingkittty!

    From your sketch, I will assume that the layout looks like this:
    Code:
          E       D       C
          *       *       *
    
                  *
                  A
                          *
                          B
    I further assume that E,D,C are collinear
    . . and that E,A,B are collinear.


    Consider points A,B,C,D,E as shown.

    1. If two of these points are selected at random,
    what is the probability that they are collinear?
    There are: . {5\choose2} \:=\:10 pairs of points.

    Any two points are collinear.
    . . Hence, there are 10 pairs of collinear points.

    Therefore: . P(\text{2 points collinear}) \:=\:\frac{10}{10}\:=\:1



    2. If three of these points are selected at random,
    what is the probability that they are collinear?
    There are: . {5\choose3}\,=\,10 sets of three points.

    There are 2 sets which are collinear: . EDC,\:EAB

    Therefore: . P(\text{3 points collinear}) \:=\:\frac{2}{10} \:=\:\frac{1}{5}



    3. If four of these points are selected at random,
    what is the probability that they are collinear?
    There are: . {5\choose4} \,=\,5 sets of four points.

    There are no sets of four points that are collinear.

    Therefore: . P(\text{4 points collinear}) \:=\:\frac{0}{5} \:=\:0

    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Sep 2007
    Posts
    8
    Thank You for the help. I'm still confused on how do you find out how many pairs of points there are.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. collinear points
    Posted in the Geometry Forum
    Replies: 18
    Last Post: May 3rd 2009, 08:13 AM
  2. Collinear Points
    Posted in the Geometry Forum
    Replies: 1
    Last Post: April 19th 2008, 05:04 PM
  3. A, B, C, D are collinear points
    Posted in the Geometry Forum
    Replies: 1
    Last Post: November 20th 2007, 12:30 AM
  4. Collinear points
    Posted in the Geometry Forum
    Replies: 2
    Last Post: December 26th 2006, 09:46 PM
  5. Five collinear points
    Posted in the Geometry Forum
    Replies: 0
    Last Post: September 11th 2006, 03:20 AM

Search Tags


/mathhelpforum @mathhelpforum