Final answer:
MN has two possible values depending on M's position: 7 units if M is between L and N, or 33 units if N is between L and M, because L, M, and N are collinear.
Step-by-step explanation:
Since points L, M, and N are collinear, this means they lie on the same straight line. Given that LM is 13 units and LN is 20 units, we can determine a possible value for MN by understanding that the distance between two points on a line is the absolute difference of their distances from a common point.
If M is between L and N, MN would be LN - LM, which is 20 - 13. Therefore, MN would equal 7 units. However, if M is not between L and N, and N lies between L and M, then MN would be the sum of LM and LN, which is 13 + 20, giving us MN equaling 33 units.
The possible value of MN can be either 7 units or 33 units, depending on the position of M relative to L and N on the straight line.