# Thread: Finding Vertices of a Parallelepiped

1. ## Finding Vertices of a Parallelepiped

I will try to describe the picture:

The figure is a rectangular box, with the near lower left point A labeled (3,3,4) and the far top right point B labeled (-1,6,7).

I am to find the coordinates of the remaining 6 vertices. There are no examples in my book, and I'm not sure how to solve. I have found |A|= root 34, |B| = root 86, and |AB| = root 34.

2. Originally Posted by veronicak5678
I will try to describe the picture:

The figure is a rectangular box, with the near lower left point A labeled (3,3,4) and the far top right point B labeled (-1,6,7).

I am to find the coordinates of the remaining 6 vertices. There are no examples in my book, and I'm not sure how to solve. I have found |A|= root 34, |B| = root 86, and |AB| = root 34.
View my diagram and note that, by pythagorus:

$\displaystyle |BH|^2 + |AH|^2 = |AB|^2$ (which you can see from the blue line!)

You know A and B, so you can most certainly find H from this, and then continue in that fashion to uncover the rest of the coordinates.

3. Thanks for answering and for providing a diagram.
I understand what you mean, but don't know how to solve for |BH| and |AH| using the points I have.

4. Originally Posted by veronicak5678
Thanks for answering and for providing a diagram.
I understand what you mean, but don't know how to solve for |BH| and |AH| using the points I have.
Show me your working for |AB|.

5. |AB| = root ( (-1-3)^2 + (6-3)^2 + (7-4)^2 ) = root 34

6. Delete.