Question

Select the postulate that states a line is determined by two points.

Answer 1

4. Postulate 2: Through any two different points, exactly one line exists.

Postulate 2 and Postulate 1 are the only two postulates that really make sense. Postulate 2 is your answer instead of Postulate 1 for the following reason:

Postulate 1 states that a line contains at least two points.
Postulate 2 states that through any two different points, exactly one line exists.

Postulate 1 says that all lines contain at least two points, while Postulate 2 says that two points contain a line.

Answer 2

Answer: The answers are postulate 1 and postulate 2.

Step-by-step explanation: We know that given any two points, we can always draw a line passing through them. Also, we can find the equation of the line with the help of these two points, which gives all the points lying on it.

Out of the given 7 postulates,

Postulate 1 states that a line contains at least two point, which is correct and can be used in place of actual definition of a line. So, this option is correct.

And, postulate 2 states that through any two different points, exactly one exists, which can also replace the definition of a line and hence it is also correct.

See the attached figure, we have only two points A and B, through which the line AB is drawn.

The other postulates does not give us the analogue of our given statement and so we cannot consider them to be right.

Thus, the correct option are Postulate 1 and postulate 2.