Trapezoid Vectors

Date: 9/9/95 at 0:12:45
From: Anonymous
Subject: Algebra Geometry - Vectors

Dr. Math, I've been trying to get this one for hours....

Please help....

In a trapezoid TXYZ, the vector TX = the vector bZY.  If the diagonals
meet at O, find an expression for the vector TO in terms of the 
vector TX and the vector TZ.

Thanks in advance.

Shailesh Lakhani

Date: 9/29/95 at 16:56:44
From: Doctor Andrew
Subject: Re: Algebra Geometry - Vectors
 
   X____Y
   /    \ 
  /______\
 T         Z

If this diagram is wrong, my solution may still help.

To solve this problem, you could put T at the origin and then find
the values of the corners of the trapezoid in terms of ZY and TZ
which you should probably call something else (a and c maybe).  Once you
have those points you can write equations for the diagonals and find
the point of the intersection.  

Once you've got the point of intersection, you can set up two equations,
one for x and one for y, that add the values of TX and TZ to get O.  You
don't need to worry about angles.  Just think of a vector as being a
value (x,y) where x^2 + y^2 = length^2.

-Doctor Andrew,  The Geometry Forum