Results 1 to 5 of 5

Math Help - Vectors/Triangle Help Please

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    49

    Vectors/Triangle Help Please

    Here are the questions:

    1.)

    In the triangle ABC, let M and N be the midpoints of AB and AC respectively. Show that vector MN is equal to one-half of vector BC. Conclude that the line segment joining the midpoints of two sides of a triangle is parallel to the third side. How are their lengths related?

    2.)

    Use vectors to prove that the midpoints of the four sides of an arbitrary quadrilateral are the vertices of a parallelogram.

    Thanks A Lot
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,252
    Thanks
    5
    1) \overrightarrow{MN}=\overrightarrow{MA}+\overright  arrow{AN}=\frac{1}{2}\overrightarrow{BA}+\frac{1}{  2}\overrightarrow{AC}=

    =\frac{1}{2}(\overrightarrow{BA}+\overrightarrow{A  C})=\frac{1}{2}\overrightarrow{BC}

    The vectors \overrightarrow{MN} and \overrightarrow{BC} are colinear, then MN\parallel BC

    |\overrightarrow{MN}|=\left|\frac{1}{2}\overrighta  rrow{BC}\right|\Rightarrow MN=\frac{1}{2}BC

    2) Use the first problem in the triangles formed by three vertices of the parallelogram.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2009
    Posts
    49
    Thanks for the reply,

    I tried using your logic for the 2nd problem but I keep getting the wrong answers. I think im messing up the vector addition

    Could you please give a brief explanation for the 2nd problem?

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,252
    Thanks
    5
    Let ABCD be the parallelogram, M the midoint of AB, N the midoint of BC, P the midoint of CD, Q the midpoint of DA.

    Use the problem 1 in the triangle ABC with the points M, N, then in the triangle CDA with the points P, Q.

    You'll get that MN and PQ are parallel to AC and their length is half of AC. So MNPQ is a parallelogram.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Jan 2009
    Posts
    591
    Quote Originally Posted by red_dog View Post
    Let ABCD be the parallelogram, M the midoint of AB, N the midoint of BC, P the midoint of CD, Q the midpoint of DA.

    Use the problem 1 in the triangle ABC with the points M, N, then in the triangle CDA with the points P, Q.

    You'll get that MN and PQ are parallel to AC and their length is half of AC. So MNPQ is a parallelogram.
    This just provided insight to the solution of a problem.
    Thanks.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. height of the triangle over the vectors
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: January 11th 2012, 04:18 AM
  2. vectors: right triangle
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 24th 2010, 12:19 PM
  3. area of triangle using 3d vectors
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 25th 2009, 03:35 PM
  4. [SOLVED] Triangle & vectors
    Posted in the Geometry Forum
    Replies: 1
    Last Post: September 25th 2008, 10:53 PM
  5. Triangle defined by vectors
    Posted in the Advanced Math Topics Forum
    Replies: 3
    Last Post: August 16th 2005, 10:54 AM

Search Tags


/mathhelpforum @mathhelpforum