Question

if possible, use the law of detachment to make a conclusion. if it is not possible to make a conclusion, tell why. if three points are on the same line, then they are collinear. points x, y, and z are on line k. choose the correct answer below. a. the conclusion is the points x, y, and z are collinear. b. the conclusion is the points x, y, and z are coplanar. c. it is not possible to make a conclusion using the law of detachment because the second statement does not match the conclusion of the given conditional statement. d. no conclusion is possible because the hypothesis given is not the same as the hypothesis of the given conditional statement.

Explanation:

Step1: Recall Law of Detachment

The Law of Detachment states that if a conditional statement “if p, then q” is true and p is true, then q is true.
The conditional statement is “If three points are on the same line, then they are collinear.” Here, p is “three points are on the same line” and q is “they are collinear”.

Step2: Analyze given statements

We are given that points X, Y, and Z are on line k. This means the hypothesis p (three points are on the same line) is satisfied for points X, Y, and Z.

Step3: Make conclusion

By the Law of Detachment, since the conditional statement is true and the hypothesis is true for points X, Y, and Z, the conclusion q (they are collinear) is true for points X, Y, and Z.

Answer:

A. The conclusion is the points X, Y, and Z are collinear.