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February 28th, 2008, 11:01 PM   #1
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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.
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February 29th, 2008, 09:00 AM   #2
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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
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February 29th, 2008, 05:43 PM   #3
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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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