How do I find the other corners of this square?

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Homework Help Overview

The discussion revolves around finding the coordinates of points B and D of a square, given points A and C. The problem involves understanding the properties of squares, particularly the relationships between the diagonals and the coordinates of the vertices.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the properties of the diagonals, including their intersection and perpendicularity. There are attempts to calculate the coordinates of B and D using the midpoint of AC and the distance from this point. Questions arise about how to apply the dot product and the distance formula effectively.

Discussion Status

The discussion is ongoing, with participants sharing insights about the properties of squares and the relationships between the coordinates. Some guidance has been provided regarding the use of the distance formula and the properties of the diagonals, but there is no clear consensus on the next steps to take.

Contextual Notes

Participants are working under the constraints of using only the given points A and C, and there is uncertainty about how to derive the coordinates of B and D from the information available.

I dun get it
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[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.
 
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What do you know about the intersection of the diagonals?

ehild
 
They're perpendicular. I don't know how the dot product can help in this situation.
 
I mean the point of intersection. Can you calculate its coordinates?

ehild
 
I would assume the point of intersection is half of AC which is (5.53615,-13.13056,4.176025)
 
And also half of DB, isn't it?

ehild
 
Yes, but how do I go about finding the coordinates of D and B with it?
 
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
 
So I use pythagoras to find the length of AB and from there use the dot product to find the coordinates of B?
 
  • #10
Go ahead. Let me see what you do.

ehild
 
  • #11
It did not work at all.
 
  • #12
I see. Won't you try?

ehild
 
  • #13
Try what? I'm not sure what to do to get the equations for the x and y coordinates.
 
  • #14
Diagonals of a square are congruent, and they intersect at their midpoints. You can Pythagoras' from there.
 
  • #15
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
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
But how?
 
  • #18
[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?
 
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