I'm not sure what this problem is asking me to do...

Question

163.If M is the midpoint of segment AB, how are vectors AM, AB, MB, and BM related?

Answer 1

Does this sketch help?

The vectors are denoted with the partial arrow designator. They point in the direction of the last letter. Each vector has a magnitude (length) and a direction. So you can see that vector AM and vector MB are equal to each other. But vector BM is in the opposite direction so vector AM equals negative vector BM. And vector AB equals two times vector AM.

Answer 2

Answer 3

This question is testing your understanding of what a midpoint is, and also vectors. In other words, they could have asked "What is a midpoint?" and "What is a vector?".

By definition of a midpoint (M), AM = MB 2 X AM = AB and 2 X MB = AB

By definition of a vector having direction & magnitude (length of the segment), MB and BM are equal (magnitude) and opposite (directionally)