Results 1 to 2 of 2

Math Help - Area triangle using determinant

  1. #1
    Member
    Joined
    Oct 2009
    Posts
    202

    Area triangle using determinant

    In the accompanying figure ,the area of the triangle ABC can be expressed as

    Area ABC = Area ADEC + Area CEFB - Area ADFB
    Use this and the fact that the area of trapezoid equal of the altitude times the sum of the parallel sides to show that


    Area ABC=\frac{1}{2}\left(\begin{matrix} x_1 &y_2 &1\\x_2 &y_2 & 1 \\x_3 &y_3&1\end{matrix}\right)

    [Note-in the derivation of this formula, the vertices are labelled such that the triangle is traced counter-clockwise proceeding from (x_1,y_1) to (x_2,y_2) to (x_3,y_3) .for a clockwise orientation, the determinant above yields the negative of the area.]
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member MacstersUndead's Avatar
    Joined
    Jan 2009
    Posts
    291
    Thanks
    32

    Re: Area triangle using determinant

    \frac{1}{2}\left(\begin{matrix} x_1 &y_2 &1\\x_2 &y_2 & 1 \\x_3 &y_3&1\end{matrix}\right)

    You could always expand this, re-arrange and see if you get a form that is equal to Area ADEC + Area CEFB - Area ADFB. In that case, you are done...
    Last edited by MacstersUndead; November 14th 2012 at 01:05 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Why determinant gives area enlargement?
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: July 8th 2009, 02:47 PM
  2. Replies: 1
    Last Post: October 28th 2008, 07:02 PM
  3. Replies: 7
    Last Post: July 19th 2008, 06:53 AM
  4. The area of a triangle within a triangle
    Posted in the Geometry Forum
    Replies: 4
    Last Post: April 28th 2008, 03:27 AM
  5. Replies: 27
    Last Post: April 27th 2008, 10:36 AM

Search Tags


/mathhelpforum @mathhelpforum