Math Is Fun Forum

elpuerco

Member

Registered: 2007-06-11

Posts: 2

Getting 2D point coordinates at a given perpendicular distance....

Hi Folks,

I'm trying to get a method to get a 2d point coordinates at given perpendicular distance to a known 2D point in a line like the figure showed.

Thanks in advance

Nicolas Zaragoza

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Getting 2D point coordinates at a given perpendicular distance....

You're given the direction vector for line L, and you're also told that the line from P1 to P is perpendicular to L and so that means that you can work out the direction vector from P1 to P.

If v = ai + bj, where i and j are perpendicular unit vectors in the plane, then the direction vector from P1 to P is given by (-b)i + aj.

That just tells you the direction. To make it the correct length, you first scale it to be a unit vector by dividing by its magnitude, then you multiply by the given d.

After you find P1-->P, you can use that along with the position vector P1 to calculate the position vector P.

Hopefully I've explained it well enough for you to understand what I mean. Feel free to post again if I've just confused you even more.

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Why did the vector cross the road?
It wanted to be normal.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Getting 2D point coordinates at a given perpendicular distance....

I'll call the slope of the known line V.
The P1 point I'll coordinate as (XP1,YP1).
Then, I get this for P.
(XP,YP) = ( XP1 - (Vd/(V^2 + 1)^0.5)  ,   YP1 + (d/(V^2 +1)^0.5))

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igloo myrtilles fourmis

elpuerco

Member

Registered: 2007-06-11

Posts: 2

Re: Getting 2D point coordinates at a given perpendicular distance....

Thank you very much to all of you..... it'was very helpful to me. I'm wondered the fast you respond to me!!!