Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



Re: formula for finding end point(x2,y2) of a line
Posted:
Aug 28, 2008 1:00 PM


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.



