Question

1. does c determine a specific line in the model? explain.
2. does cd determine a specific line in the model? explain.
3. does m determine a specific line in the model? explain.
4. how many points are needed to determine a specific line?
5. what is an alternate name for line ab?
6. name 3 collinear points in the model.
7. name 3 non - collinear points in the model.

Explanation:

Step1: Recall line - determination principle

Two distinct points determine a unique line.

Step2: Analyze each sub - question

5.

Point C alone does not determine a specific line. A single point can be part of infinitely many lines. So, the answer is no.

6.

Two distinct points C and D determine a unique line CD. So, the answer is yes.

7.

A line is determined by two points. A single line m is just a label for a line that is already determined by two points on it. Just the name of the line does not determine a new specific line in the sense of the two - point principle. So, the answer is no.

8.

Two points are needed to determine a specific line according to the fundamental postulate in geometry.

9.

Alternate names for line AB could be line BA, or any two points on the line can be used to name it. For example, if there are other points on line AB, we could potentially name it using those points as well.

10.

Three non - collinear points in the model could be A, C, E. (There are other possible combinations as well).

11.

Three non - collinear points could be A, C, E (answers may vary).

Answer:

1. No
2. Yes
3. No
4. Two points
5. Line BA (and other names using points on the line)
6. A, C, E (answers may vary)
7. A, C, E (answers may vary)