Joey plots a point P on the line AB, as shown.

Which statement is true?
Answer
A:There are only two points on the line AB because a postulate states that a line is drawn through two points.
B:There is only one point on the line AB because a theorem states that a line extends on both sides of a point.
C:There is at least one more point beside point P on the line AB because a postulate states that a line contains at least two points.
D:There is only one point on the line AB because a theorem states that a line joining two points lies on the plane containing one of the points.

There are 3 points on line AB:

Point A, P, and B.

Answer: C.

To find the correct answer, let's consider the information provided.

The question asks about a point P plotted on the line AB. The options provided are based on postulates and theorems involving lines and points.

To determine the correct answer, we need to understand the definitions and properties of lines and points.

A line is an infinite set of points that extends infinitely in both directions. It contains at least two points. This is a defining property of a line.

A point, on the other hand, is a single location in space. It has no size or dimension. A line can contain an infinite number of points.

With this understanding, let's evaluate the options:

A: "There are only two points on the line AB because a postulate states that a line is drawn through two points." This statement is incorrect. A line contains at least two points, but it can have infinitely many points.

B: "There is only one point on the line AB because a theorem states that a line extends on both sides of a point." This statement is also incorrect. A line extends infinitely in both directions, so there are infinitely many points on the line, not just one.

C: "There is at least one more point besides point P on the line AB because a postulate states that a line contains at least two points." This statement is correct. As mentioned earlier, a line contains at least two points, so there must be at least one more point on line AB besides point P.

D: "There is only one point on the line AB because a theorem states that a line joining two points lies on the plane containing one of the points." This statement is incorrect. The theorem states that a line joining two points lies on the plane containing both of those points. It does not imply that there is only one point on the line.

Based on the explanations above, the correct answer is C: "There is at least one more point besides point P on the line AB because a postulate states that a line contains at least two points."