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November 9th, 2011, 05:39 AM  #1 
Newbie Joined: Nov 2011 Posts: 2 Thanks: 0  find a point on the border of a rectangle.
Greetings, I have a question I would like to ask; is it possible to calculate the green point in the image I made below? And if so... how? Given are the blue points P1 and P2 and the pink point p3 and the width W and height H of the pink square. Thanks in advance! Marnix van Rijswijk. 
November 9th, 2011, 06:44 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,923 Thanks: 1123 Math Focus: Elementary mathematics and beyond  Re: find a point on the border of a rectangle.
Are you able to calculate the equation of the line through P1 and P2?

November 9th, 2011, 07:18 AM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,923 Thanks: 1123 Math Focus: Elementary mathematics and beyond  Re: find a point on the border of a rectangle.
I'll assume you have some sort of xy coordinate system set up. We can use an equation in the form y = m * x + b, where m is the slope of the line, (its gradient) and b is its yintercept, (where the line crosses the yaxis). m = (P1y  P2y)/(P1x  P2x). Now, to find b we use P1y = m * P1x + b, b = P1y  m * P1x. So, to get the coordinates of the green point (Gx, Gy), we use Gx = P3x and Gy = m * P3x + b. 
November 9th, 2011, 01:09 PM  #4  
Global Moderator Joined: May 2007 Posts: 6,710 Thanks: 675  Re: find a point on the border of a rectangle. Quote:
 
November 10th, 2011, 01:56 AM  #5 
Newbie Joined: Nov 2011 Posts: 2 Thanks: 0  Re: find a point on the border of a rectangle.
Ah sorry, yes the sides are parallel to the axes, although if you know an answer to calculate this with a rectangle that's not parallel to the axes I'm all ears. And yes I'm using an x,y coordinate system. 
November 10th, 2011, 01:13 PM  #6  
Global Moderator Joined: May 2007 Posts: 6,710 Thanks: 675  Re: find a point on the border of a rectangle. Quote:
 

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