Do I Have To Explicitly Define Points/Lines/Planes? The problem I was given is as follows:

Assignment:  Draw and label the following figures.
Two planes that do not intersect. Lines  LM  and  NP  on the same plane
  (coplanar) but do not intersect. Points X and Y lie on line  AB .

My submitted answer was as follows:

This is online high school and these were the comments left by my teacher:

1) Since planes extend infinitely, I cannot tell whether or not plane R will intersect with plane S -1 point
2) You did not draw any lines (you just placed points L, M, N, and P somewhere in a plane) -5 points
3) Once again, you do not have a line!  If you would have drawn a line, it looks like points X and Y would fall on line AB, but I can't
  give you points because "I think" you understand what was asked.  You
  must show me -5 points

Here is my frustration:

I am not convinced that his comments, or point deductions are valid!
  To address his first comment, I just used some common sense and found
  that there really is no way to illustrate two planes on a different Z
  axis without showing the objects from a perspective view (rather than
  an orthographic view). (This is my experience with 3d software
  speaking) Am I wrong?
Addressing the second and third point: Being that lines/planes/etc are
  just the relations between points, isn't my illustration still
  correct?

I just started this course and I'm starting to wonder if I am as stupid as this teacher makes me feel with his comments on this assignment; or if he is being ridiculous. Either way, I'll learn something new.
 A: *

*Yes, the drawing is unclear, and yes, using a perspective view would likely have made things clearer. In particular a perspective view where you could see the planes intersecting the axes of some coordinate system in different positions.
Another way might have been drawing the planes in such a way that they partially hide one another, to demonstrate that they are in different heights. Then the fact that the section you draw is drawn parallel might be taken to indicate that the planes are parallel as well, so they will never intersect. This might even work in the orthographic setup.


*Yes, drawing of the lines was part of the task.


*Here one might have more success in arguing that “line $AB$” was part of the constraints for $X$ and $Y$, but that the position of $X$ and $Y$ themselves was what you'd have to draw. But that argument fails since $A$ and $B$ were not given either, and not drawing them makes no sense at all. So when you draw $A$ and $B$, then drawing the line joining them as well seems only reasonable.
On the whole, I'd say the judgement was justified. Whether it was appropriate depends on how many points there were to be gained over all, since you do demonstrate understanding of the issues at hand. But instead of confronting someone over this score, I'd rather suggest you see this as an indication of the kind of work that will be expected from you in this course, and try to adapt to that expectation. That way, you can work with the teacher instead of against him, which will make the whole course much more profitable to you.
