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February 28th, 2008, 11:01 PM  #1 
Newbie Joined: Feb 2008 Posts: 2 Thanks: 0  Help : Extending line by a length
I am trying to do function in C to calculate extending line by a length. While I think the formula probably something to do with Pythagoras' theorem, I can't figure it out. Given a straight line, from point A to point B , I want to extend the line by certain length (from point B to point C). For example A => (5, 11) B => (12, 15) Length = 7, what is point C ? Thanks. 
February 29th, 2008, 09:00 AM  #2 
Member Joined: Feb 2008 From: Dayton, OH, USA Posts: 33 Thanks: 0 
Let us call the x and y components in each of the ordered pairs as follows: A = (Ax, Ay) B = (Bx, By) C = (Cx, Cy) Now let us call the slope of the line m and it can be obtained from points A and B: m = (By  Ay) / (Bx  Ax) = (Cy  By) / (Cx  Bx) And suppose we want to extend the line by length L from point B to C, we know that: L² = (Cx  Bx)² + (Cy  By)² Using these two equations we can derive expressions for Cx and Cy in terms of known quantities. I won't go through the algebra here but the results are: Cx = L / √(m² + 1) + Bx Cy = L*m / √(m² + 1) + By Thus plugging in the numbers for your example gives: Cx = 49/√65 + 12 Cy = 28/√65 + 15 
February 29th, 2008, 05:43 PM  #3 
Newbie Joined: Feb 2008 Posts: 2 Thanks: 0 
Interesting solution. Yesterday a friend of mine suggest another way of calculating extended line. This have to do with Pythagoras' theorem, the idea is finding the unit of hypotenuse affected by width and height. W = Width H = Height Hypo = hypotenuse W = Bx  Ax H = By  Ay Hypo = sqrt((W * W) + (H * H)) // square root of ((W * W) + (H * H)) Cx = (W / Hypo) * (Hypo + Length) Cy = (H / Hypo) * (Hypo + Length) I tried this formula via program simulation, rotating extended straight line by 10 degrees each step until it reach 360 degrees. It works. 

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