if a point in a three-dimention system is labled with the coordinates(1,2,-) what is the z coordinate?

Question

a. 1 b. -1 c.2 d.-2

Answer 1

(x,y,z)
its probabaly -1 or -2 because you hve not written it clearly

Answer 2

It can be anything.

The only valid answer I can dream up is:
"z is the shortest distance from the point to the x-y plane."

You need some condition to help you pick an actual value.

For example, if you are given the distance D from the origin, then use D^2 = x^2 + y^2 + z^2 to find z.

If you are given the equation of the plane that contains the point:
ax + by + cz + d = 0
then find z = -(ax + by + d)/c

If z is a function of x and y, then use the function to find z:

f(x,y) = ax^2 + bxy + cy^2 + d
then z = f(1,2) = a(1^2) + b(1*2) + c(2^2) + d

and so on

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It could be (and that would not be a very clear notation) that (1,2,-) indicates a line: "all the points where x=1 and y=2" -- the dash for z indicating that you can put anything you want. In such a case, (1,2,-) would indicate a line parallel to the z axis and going through the x-y plane at (x,y) = (1,2).
However, that also does not help you to pick one of 4 answers.

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I suspect that there is something else (an equation or a word problem) somewhere else -- either above of below the actual question -- and that you are supposed to answer the question in the context of that something else.

Answer 3

I'd assume it to be zero. It probably doesn't matter anyway.