Final answer:
The length of the line segment AB is 6 units.
Step-by-step explanation:
The length of line segment AB can be found by subtracting the coordinates of point A from the coordinates of point B. Given that AB = 9x - 3 and AM = 3x + 3, we can equate AB and AM:
9x - 3 = 3x + 3
6x = 6
x = 1
Substituting x = 1 back into AB = 9x - 3:
AB = 9(1) - 3 = 9 - 3 = 6
Therefore, the length of line segment AB is 6 units.