# Cartesian coordinates

1. Mar 25, 2004

### Ralgar

Hi. I was just wondering if anyone could help me with a formula to solve the following problem.

I have two locations (L1 and L2), which I know the cartesian coordinates of, situated in a three dimensional space. I also have a distance (D) which I also know the value of. D is not the distance between L1 and L2. If an object moves from it's starting location at L1 in a straight line towards L2, how do I calculate the cartesian coordinates of the object after it has travelled a distance of D units.

I'd certainly appreciate any assistance in this.

Cheers.

2. Mar 26, 2004

### HallsofIvy

Staff Emeritus
Let L1= (x1,y1,z1) and
L2= (x2,y2,z2).

Let d= distance from L2 to L1= [sqrt]((x2-x1)2+(y2-y1)2+(z2-z1)2).

The any point on the line through L2 and L1 has coordinates
x= x1+ (x2-x1)(t/d)
y= y1+ (y2-y1(t/d)
z= z1+ (z2-z1)(t/d)

(notice that when t= 0, this is x= x1 and when t= d, this is x= x2, etc.)

In particular, taking t= D will give the coordinates of the point at distance D from L1 in the direction of L2.

3. Mar 26, 2004

Thank you.