Arrange the reasons for the proof in the correct order. prove: if two points are collinear, then the two points lie on the same line. a. by definition, the two lines are not collinear. b. if two points do not lie on the same line, then they are not collinear. therefore, if two points are collinear, then they lie on the same line (proof by contraposition). c. assume that the two points lie on different lines. a. a, c, b b. b, c, a c. c, a, b d. c, b, a

C)   The correct order of the proof is C , A , and B.

Step-by-step explanation:

Here,the given problem is

To Prove: If two points are co-linear, then the two points lie on the same line.

Proof is given as:

A. By definition, the two lines are not collinear.

B. If two points do not lie on the same line, then they are not collinear. Therefore, if two points are collinear, then they lie on the same line (proof by contraposition).

C. Assume that the two points lie on different lines.

Here, the correct order of the solution is

ASSUME THE CONTRADICTION:

C. Assume that the two points lie on different lines.

APPLY THE DEFINITION of Co linearity

A. By definition, the two lines are not co linear.

ARRIVE AT A CONTRADICTION:

B. If two points do not lie on the same line, then they are not co linear. Therefore, if two points are co linear, then they lie on the same line

hence, the proof.

Hence, the correct order of the proof is B , C , and A.