Co-ordinates of four points on the lower surface of the recanguler box are
(1,2,3), (1,5,3), (7,5,3) and (7,2,3)
Similarly can you find the co-ordinates of the four points on the upper surface of the rectangular box?
The faces of a rectangular box are parallel to the coordinate planes. Two of the vertices are at the points (1,2,3) and (7,5,4).
*Draw the box and label the vertices
Since it said the faces of the box are parallel to the coordinate planes, I tried finding 2 more vertices parallel to the z-axis. I said the point (1,2,3) on the other side of the z-axis = (1,-2,3) (red) since all y points are negative there and used the same reasoning for the point (7,5,4) (blue). However if I try to join the points (1,2,3), (1, -2, 3), (7,5,4) and (7,-5,4) together, I dont get a rectangular face on the z-axis (yellow). The orange and green line shows how I drew the points (7,-5,4) and (1,-2,3) respectively.
What have I done wrong?
Oh ok I understand that. I made a rough sketch of the rectangular box and got the 4 points for the one face. Like you said for the z-coordinates on the other side of the top surface = 4 (blue x), but how would you determine its x and y coordinate (also for the bottom surface with constant z = 3 (yellow x)?)
Hello, SyNtHeSiS!
The faces of a rectangular box are parallel to the coordinate planes.
Two of the vertices are at the points (1,2,3) and (7,5,4).
Draw the box and label the vertices.
Don't try to make a sketch now . . . wait until the end.
The two points are diametrically opposite vertices.
. . Since goes from 1 to 6, the length of the box is 5.
. . Since goes from 2 to 5, the width of the box is 3.
. . Since goes from 3 to 4, the height of the box is 1.
Consider the "bottom" of the box.
All four vertices of this rectangle have
Plot the points on a two-dimensional graph.
Code:| |(1,5,3) 6 (7,5,3) | * → → → → → → → → → → → * | ↑ ↑ | ↑ ↑ | 3↑ ↑3 | ↑ ↑ | ↑ ↑ | * → → → → → → → → → → → * |(1,2,3) 6 (7,2,3) | | - - + - - - - - - - - - - - - - - - - - - |
We start at (1,2,3).
We know the length is 6, so we move right 6 units . . . to (7,2,3).
We know the width is 3, so we move up 3 units . . . to (1,5,3).
And we do both: move right 6 units, up 3 units . . . to (7,5,3).
And we have the coordinates of the bottom of the box:
. .
Since the height of the box is 1, add 1 to the -coordinates.
And we have the corordinates of the top of the box:
. .
Now I can draw the box . . . and then label the coordinates.
Code:(1,2,4) (1,5,4) * - - - - - * / /| / / | / / *(1,5,3) / / / / / / / / / / / / (7,2,4)* - - - - - *(7,5,4) | | / | |/ * - - - - - * (7,2,3) (7,5,3)
And the unseen vertex (in the back) is
Thanks a lot, that post helped a lot. I tried to draw the box, but I am having a problem projecting the surfaces through the z-axis. Referring to the attachment I drew the bottom surface in R3 with the coordinates: (1,5,0), (7,5,0), (1,2,0) and (7,2,0), then I tried projecting these points up by 3 to get (1,5,3), (7,5,3), (1,2,3) and (7,2,3), but they all lie on the line z = 3 (in blue) and look like a line as opposed to a plane