Re: Find point given 2 points

From: Michael Hill (hillmw_at_ram.lmtas.lmco.com)
Date: 06/28/04 

Date: Mon, 28 Jun 2004 12:43:18 -0500
To: Lynn Kurtz <kurtzDELETE-THIS@asu.edu>

> >Two questions about finding the 3rd point:
> >
> >I have a line consisting of the coordinates (4,6) and (12,2).
> >The midpoint of the line can be calculated as (8,4) using the
> >midpoint formula.
> >A right triangle is formed at the midpoint (8,4).
> >
> >1) Using 2 points (8,4) and point (12,2) and the lengths of the legs
> >I'd like to find the 3rd point.
> >
> >Assume the following data:
> >The small leg of the triangle is formed from (8,4) to (12,2) (call
> >this leg b).
> >The large leg of the triangle has a length of 10 (call this leg a).
>
> Leg a lies along the vector < 4, -2 >.

Did you arrive at this mathematically or by drawing a graph?

>Leg b lies along the direction
> of the perpendicular vector < 1, 2>.

How is this important?

>Make a unit vector out of this by
> dividing by its length: u = (1/sqrt(5))< 1, 2>. The third point is 10
> units in this direction from (8, 4) so its position is:
>
> < 8, 4 > + 10/sqrt(5)< 1, 2 > = < 8 + 2 sqrt(5), 4 + 4 sqrt(5) >

I need a formula where the unknowns x` abd y` are calculated using our
known vars.

Appreciate your help.

Mike

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