Results 1 to 7 of 7

Math Help - Proving quadrilateral is a rectangle algebraically

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    4

    Proving quadrilateral is a rectangle algebraically

    How do you prove algebraically, that the following vertices are a rectangle. I can plot it on a graph, but I can't figure out how to prove using algebra.

    Help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    Quote Originally Posted by GR9STUDENT View Post
    How do you prove algebraically, that the following vertices are a rectangle. I can plot it on a graph, but I can't figure out how to prove using algebra.

    Help.
    Would you happen to have the vertices in question? We typically look for equal lengths and equal slopes...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2010
    Posts
    4
    Sorry, I did not list the vertices, they are (1,0) (-1,5) (4,7)(6,2)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    Quote Originally Posted by GR9STUDENT View Post
    Sorry, I did not list the vertices, they are (1,0) (-1,5) (4,7)(6,2)
    1 way to do it:

    Let the given points correspond to A,B,C,\text{ and }D respectively.

    Then to show that ABCD is a rectangle, we must show that each interior angle measures 90^{\circ} . To do this, we must need to only compare the slopes of line segments AB with BC, and BC with CD and etc...

    Do you get what I'm saying?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jan 2010
    Posts
    4
    No, I am lost on this one.

    I understand that the rectangle has four 90 angles, and that the slope of each pair of lines will equal each other. But I don't know how to show with forumula.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    Quote Originally Posted by GR9STUDENT View Post
    No, I am lost on this one.

    I understand that the rectangle has four 90 angles, and that the slope of each pair of lines will equal each other. But I don't know how to show with forumula.
    OK.

    Perpindicular lines will have slopes that are the negative recirocal respective to each other.

    So AB has slope m_1=\frac{5-0}{-1-1}=-\frac{5}{2}

    and BC has slope m_2=\frac{7-5}{4-(-1)}=\frac{2}{5}

    Now, since -\frac{1}{m_1}=m_2 it follows that AB is perpindicular to BC.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Jan 2010
    Posts
    4

    Smile

    Thankyou, that makes sense.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: June 1st 2011, 01:40 PM
  2. Replies: 1
    Last Post: February 19th 2011, 04:19 AM
  3. Proving a field is not algebraically closed
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: April 13th 2009, 10:10 AM
  4. Replies: 1
    Last Post: September 10th 2008, 02:59 PM
  5. Proving a quadrilateral is a rectangle?
    Posted in the Geometry Forum
    Replies: 8
    Last Post: January 22nd 2008, 06:11 PM

Search Tags


/mathhelpforum @mathhelpforum