Question

Points L,M and N are collinear You are given LM=8 and LN = 18 what is possible value of MN

Answer 1

Since points L, M, and N are collinear, we can consider different arrangements of these points to find the possible values for MN. There are two main arrangements to consider:

1. **Arrangement with M between L and N**:
In this case, we have:
\[
LN = LM + MN
\]
Substituting the given values:
\[
18 = 8 + MN
\]
Solving for MN:
\[
MN = 18 - 8 = 10
\]

2. **Arrangement with N between L and M**:
In this case, we have:
\[
LN = LM - MN
\]
Again substituting the given values:
\[
18 = 8 - MN
\]
Solving for MN gives:
\[
MN = 8 - 18 = -10
\]
Since a distance cannot be negative, this arrangement is not valid.

3. **Arrangement with L between M and N**:
In this case:
\[
LN = MN + LM
\]
Substituting the values:
\[
18 = MN + 8
\]
Solving for MN:
\[
MN = 18 - 8 = 10
\]

Considering all the arrangements, the only valid positive distance for MN is:
\[
\boxed{10}
\]

Thus, the possible value of MN is 10.