Question

Points P, M, and T are on a line, and PT - PM = MT. Which point is between the other two? Explain your answer.

A) P, because it's equidistant from both M and T.
B) M, because it's the midpoint between P and T.
C) T, because it's equidistant from both P and M.
D) None of the above, as the information provided is insufficient.

Answer 1

Point M is between points P and T because PT - PM = MT implies that M is the midpoint, equidistant from both P and T on the line.

Step-by-step explanation:

If points P, M, and T are on a line, and the equation PT - PM = MT is given, we can infer the positions of the points on the line. Since PT represents the total length from P to T and PM represents the length from P to M, subtracting PM from PT essentially gives us the length from M to T, which is MT.

We know that PT is the sum of PM and MT, so if we rearrange the given equation, PT = PM + MT, then PT - PM = MT. This means that point M must be somewhere in between points P and T. Therefore, option B is correct: M is the midpoint between P and T.

This means M is equidistant from both P and T, and hence it lies between them. This conclusion is based on the properties of a line segment and basic arithmetic.