Mentor: Please draw the coordinate axis on your paper. Now label the x and y-axis. Now label each line on the x and y axis with a scale of one.
Mentor: Did you know that the coordinate axis is a plane?
Student: No. What is a plane?
Mentor: A plane is a flat surface that continues out infinitely. The best way to see what a plane is like is to imagine a piece of paper that never ends.
Student: So does infinity mean never ending?
Mentor: Yes it does. Infinity represents something that has the potential to keep going. For any given value a larger value can always be found.
Student: So a plane stretches out to the end of the universe.
Mentor: Yes, but more than that. The end of the universe represents an ending. Something that can be considered infinite does not end. In actuallity nothing that exists can be infinite. It just has the potential to continue like our number system or a line. Now, can any one remember what a line is?
Student: A line is made up of at least two points that are on a straight path.
Mentor: Yes, very good. Let's draw one.
Mentor: Now, does anyone have an idea of what a ray is?
Student: The beam of light that comes out of a ray gun.
Mentor: Good idea. A ray gun has a starting point and it goes on forever if it never hits its target. A ray starts at one point and it continues out to infinity.
Mentor: Let's draw a ray.
Student: So, what is the difference between a line and a ray?
Mentor: A line goes on to infinity in both directions, but a ray stops on one end. If you cut a line in half, you make two rays. Now, can anyone guess what a line segment is?
Student: Is it a line with two ends?
Mentor: Exactly right. A line segment is part of a line that has two endpoints. Let's draw one on paper.