Question

Points A(−1.5) and B(6) are marked on a number line. Find the coordinate of point M if it is known that AM:MB=1:2. Find all possible answers.

Answer 1

We know that A to B is equal to 6 - (-1.5), which is 7.5 in length. We also know that MB is twice as long as AM. This means 2AM=MB and AM+MB=7.5. Therefore, AM+2AM=7.5, or 3AM=7.5. Dividing out 3 from both sides shows that AM=2.5. To find point M on the number line, we can then add 2.5 to point A (the lower point on the number line, which gives us 1. M=1.