# How do I find the other corners of this square?

1. Aug 8, 2010

### I dun get it

[PLAIN]http://img713.imageshack.us/img713/6686/wtfhalp.jpg [Broken]

How do I work out points B and D with only points A and C given? B and D have the same z-coordinates. I worked out the red vector, but have no idea what to do from there.

Last edited by a moderator: May 4, 2017
2. Aug 8, 2010

### ehild

What do you know about the intersection of the diagonals?

ehild

3. Aug 8, 2010

### I dun get it

They're perpendicular. I don't know how the dot product can help in this situation.

4. Aug 8, 2010

### ehild

I mean the point of intersection. Can you calculate its coordinates?

ehild

5. Aug 8, 2010

### I dun get it

I would assume the point of intersection is half of AC which is (5.53615,-13.13056,4.176025)

6. Aug 8, 2010

### ehild

And also half of DB, isn't it?

ehild

7. Aug 8, 2010

### I dun get it

Yes, but how do I go about finding the coordinates of D and B with it?

8. Aug 8, 2010

### ehild

The intersection of the diagonals is a point of the line DB. Both D and B have the same z coordinates, what is this coordinate?
I you know the z coordinate of B, you can find two more equations to find the x and y coordinates.
You know how far B is from the centre... you know that the diagonals are normal to each other. And both D and B are at equal distance from A and C...or the vectors AC and AB enclose a 45° angle ...

ehild

9. Aug 8, 2010

### I dun get it

So I use pythagoras to find the length of AB and from there use the dot product to find the coordinates of B?

10. Aug 8, 2010

### ehild

Go ahead. Let me see what you do.

ehild

11. Aug 8, 2010

### I dun get it

It did not work at all.

12. Aug 8, 2010

### ehild

I see. Won't you try?

ehild

13. Aug 8, 2010

### I dun get it

Try what? I'm not sure what to do to get the equations for the x and y coordinates.

14. Aug 8, 2010

### thrill3rnit3

Diagonals of a square are congruent, and they intersect at their midpoints. You can Pythagoras' from there.

15. Aug 8, 2010

### I dun get it

I got the length, but how do I get the x and y coordinates of AB with it? Using the dot product doesn't really help.

16. Aug 8, 2010

### thrill3rnit3

Use the distance formula again. You have the coordinates of A, the length of AB, so you should be able to find the coordinates of B.

17. Aug 9, 2010

### I dun get it

But how?

18. Aug 10, 2010

### I dun get it

[PLAIN]http://img291.imageshack.us/img291/2650/62843747.jpg [Broken]

That's all I can do. How do I use those distances to find x and y? I know to use pythagoras, but what am I using for a, b and c?

Last edited by a moderator: May 4, 2017