The value of LM = 6.
Let's break down the given transformations for each point:
1. Original point:

2. First transformation:

3. Second transformation:
,

Now, if CD = 9 in the original triangle, LM can be found using the scale factor of
, as the second transformation involves scaling by
.
![\[ LM = (2)/(3) * CD \]\\LM = (2)/(3) * 9 \]\\LM = 6 \]](https://img.qammunity.org/2019/formulas/mathematics/middle-school/k9rmpg09cid7cdu4zj1xy0x650chs8l0n7.png)
Therefore, LM = 6.