Question

If points P, Q, and S are collinear with Q between P and S, then PS - QS = PQ. Evaluate the given statements and select the correct one:

A) P, Q, and S are collinear
B) PQ + QS = PS
C) PQ = PS - QS
D) PS - QS = PQ

Answer 1

The correct evaluation of the distances between collinear points is based on the segment addition postulate; the expression PS - QS = PQ is true and corresponds to statement D.

Step-by-step explanation:

The situation described involves three collinear points P, Q, and S with Q being between P and S. When points are collinear and arranged as described, the segment addition postulate applies. This postulate states that if point Q is between P and S, then the length of segment PQ plus the length of segment QS is equal to the length of segment PS, or formally PQ + QS = PS.

To address the statement PS - QS = PQ, you start with the segment addition postulate PQ + QS = PS and subtract QS from both sides of the equation, which results in the correct expression PS - QS = PQ. Therefore, the correct statement that evaluates the given expressions is D) PS - QS = PQ.