|
Question 566766: The textbook says:
In the drawing, P, which is a vertex of the rectangular prism, has coordinates (2,3,4) on the coordinate plane. Point Q, which is also a vertex, is located at the origin.Find the remaining six coordinates of the rectangular prism.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
I don't have your textbook, so I don't have your drawing. Use your head for something besides a hat rack next time you post a question about a drawing that we can't possibly see. Remember, this is Algebra.com -- it is not the Psychic Hot Line.
Be that as it may, the only way this will work is if point P is one endpoint of a long diagonal of the prism and point Q is the other end point and the prism is arranged so that the three edges of the prism that are orthogonal at point Q are each coincident with one of the three coordinate axes.
The next thing to realize is that a point with non-zero coordinates specified by an ordered triple is NOT in the coordinate PLANE. Planes are 2 dimensional and this is three-space. You are not in Kansas anymore, Toto.
Presuming that the  (horizontal) and  (vertical) axes are in the plane of your paper and the  axis extends out from or into the paper, then the described prism must have one surface in the  plane, one in the  plane, and the third in the  plane.
Any point that is in the plane will have a coordinate of zero. Any point in the plane will have a coordinate of zero. Any point in the plane will have an coordinate of zero. If a point is actually on the axis, the and coordinates will both be zero...and the pattern continues. All coplanar points in a plane parallel to the axis will have equal coordinates...and so on.
That is sufficient information to derive all eight ordered triples representing the vertices of the described rectangular prism.
John
My calculator said it, I believe it, that settles it
|
|
|
| |
