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Topic: formula for finding end point(x2,y2) of a line
Replies: 2   Last Post: Aug 28, 2008 1:00 PM

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Narcoleptic Insomniac

Posts: 797
From: Racine, WI
Registered: 3/10/05
Re: formula for finding end point(x2,y2) of a line
Posted: Aug 28, 2008 1:00 PM
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On Aug 28, 2008 6:05 AM CT, HallsofIvy wrote:

> On Aug 27, 2008 3:52 PM CT, nav wrote:

> > how we can find end point(x2,y2) of a line when
> > starting point(x1,y1) and length of line is given

> You can't. Draw a circle with center at (x1, y1)
> and radius equal to the lenght given. Every point
> on that circle is the end point of such a line.

HallsofIvy is right -- there is no unique end point in
this case, and the solutions form a circle.

To see this, recall that given two points (x_1, y_1) and
(x_2, y_2), the distance d between them is given by

d = sqrt[(x_2 - x_1)^2 + (y_2 - y_1)^2].

If we square both sides, we obtain

(x_2 - x_1)^2 + (y_2 - y_1)^2 = d^2

...which is the equation of a circle with center (x_1,
y_1) and radius d.

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