Determine the coordinate of point M of segment AB, if A (-6) and B (4) and AM: MB = 1: 4.

Let the required coordinate of the point M be x, then:

| 4 – (- 6) | = 10 (unit segments) – the length of the segment AB, since it is known from the condition of the problem that the coordinates of points A (- 6) and B (4);

1 + 4 = 5 (parts) – has a segment AB, into which point M divides it, since AM: MB = 1: 4;

10: 5 = 2 (unit segments) – the length of the segment AM;

Knowing that on the other hand, | x – (- 6) | = | x + 6 | (unit segments) – the length of the segment AB, we make the equation:

| x + 6 | = 2.

From the definition of the modulus of a number, we get:

x + 6 = 2 or x + 6 = – 2

x₁ = – 4;

x₂ = – 8 – does not satisfy the condition of the problem.

Answer: the coordinate of point M is (- 4).