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I have a straight that pass through the points (a,b) and (c,d). If I want to extend this length in an arbitrary value "V", how can I calculate the additional points where the straight will pass through?

Thanks a lot!

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$y-b=\frac{d-b}{c-a}(x-a)$ –  pedja Oct 11 '11 at 16:46
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1 Answer 1

One can easily construct the parametric equations of a line through the points $(a,b)$ and $(c,d)$:

$$\begin{align*}x&=(1-t)a+tc\\y&=(1-t)b+td\end{align*}$$

$t=0$ yields the point $(a,b)$, $t=1$ yields $(c,d)$, and values of $t$ outside $[0,1]$ will yield points that weren't in your original line segment...

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