# Analytical Geometry

1. Jun 14, 2009

### DERRAN

1. The problem statement, all variables and given/known data
http://img15.imageshack.us/img15/3262/30115975.png [Broken]

2. Relevant equations
all analytical methods

3. The attempt at a solution
I kinda got stuck for determining the co-ordinates of N, need some help.

Last edited by a moderator: May 4, 2017
2. Jun 14, 2009

### HallsofIvy

So you have determined where point B is? What are its coordinates?

If NBCD is a parallelogram, then N will lie on AB with the length of NB the same as the length of CD. One way to find N is to find the equation of the line through A and B, so that you have y as a function of x, use that to find the distance from a general point (x,y) on that line to B as a function of x only, set it equal to the distance from C to D and solve for x. Equivalently, treat the equation of the line through A and B and the equation of a circle with center at B, radius equal to the distance from C to D as simultaneous equations and solve for x and y.

3. Jun 15, 2009

### DERRAN

got it thanks.