Points A (-1.5) and B (6) are marked on the coordinate line. Find the coordinate of point M if you know that AM: MB = 1: 2.

Let’s find the distance between points A and B on the coordinate line.

The distance AO from point A to the zero coordinate will be 1.5 units, the distance OB from the zero coordinate to point B is 6 units.

The length of the segment AB = AO + OB = 1.5 + 6 = 7.5 units.

AM: MВ = 1: 2 – that is, the distance from point A to point M is half the distance from point M to point B.

2 * AM = BM, therefore the equality AM + 2 * AM = AB is valid.

In numerical terms, 3 * AM = 7.5, then AM = 2.5 units.

Determine the coordinate of point M.

The distance from the origin to point M is

ОМ = 2.5 – AO = 2.5 – 1.5 = 1.

Answer: M (1).