How do I find the other corners of this square?

[I dun get it]

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

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.

 

[ehild]

What do you know about the intersection of the diagonals?

ehild

 

[I dun get it]

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

 

[ehild]

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

ehild

 

[I dun get it]

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

 

[ehild]

And also half of DB, isn't it?

ehild

 

[I dun get it]

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

 

[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

 

[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?

 

[ehild]

Go ahead. Let me see what you do.

ehild

 

[I dun get it]

It did not work at all.

 

[ehild]

I see. Won't you try?

ehild

 

[I dun get it]

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

 

[thrill3rnit3]

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

 

[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.

 

[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.

 

[I dun get it]

But how?

 

[I dun get it]

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

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?