Which best describes the dimensions of a plane
a. a plane has zero dimensions because it represents a location on the coordinate plane.
b. a plane has one dimension because it is made up of an infinite number of points.
c. a plane has two dimensions because it is a flat surface that has length and width but no depth.
d. a plane has three dimensions because it is made up of exactly three noncollinear points.

We, hold up there for just a second. 

"A plane" is infinite.  Whatever direction you pick in "a plane",
the plane keeps going in that direction forever and never ends.
So "a plane" has NO dimensions.

Any PART of "a plane" has TWO dimensions, because any PART
of it that you pick occupies some length and some width.

A better way to say it is like this:

If you stick a nail into the plane at one point, THEN, to describe ANY
OTHER point in the plane relative to the nail, you need TWO NUMBERS.

THAT's why a line has one dimension, a plane has two, and a solid has
three dimensions ... it's how many numbers you need if you want to
send somebody to another point from where you're sitting.