Analytical Geometry Homework: Find Co-ordinates of N

AI Thread Summary
To find the coordinates of point N in the parallelogram NBCD, it is essential to first determine the coordinates of point B. The relationship between the lengths NB and CD is crucial, as they must be equal. One effective method involves deriving the equation of the line through points A and B, allowing for the calculation of the distance from any point (x,y) on that line to point B. This distance can then be set equal to the length of CD and solved for x. Alternatively, simultaneous equations can be used by combining the line equation with a circle equation centered at B, leading to the coordinates of N.
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Homework Statement


http://img15.imageshack.us/img15/3262/30115975.png


Homework Equations


all analytical methods

The Attempt at a Solution


I kinda got stuck for determining the co-ordinates of N, need some help.
 
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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.
 
got it thanks.
 

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