Answer
$YV = 4.5$
Work Step by Step
Theorem 6-7 states that if three or more parallel lines cut off congruent segments off of a transversal, then they will cut off congruent segments off of any transversal.
We see from the diagram that the transversals line $\overline{PS}$ is cut off in equal segments by the four parallel lines. We can then deduce that lines $VW$ and $TU$ are also transversals that are cut off in congruent segments by the same four parallel lines. We now know that $\overline{YX}$ and $\overline{XV}$ are congruent to $\overline{WY}$, so they all have lengths of $2.25$.
Since $\overline{YV}$ is made up of $\overline{YX}$ and $\overline{XV}$, we add the two segments together to find the total length of $YV$:
$YV = YX + XV$
Let's plug in what we know:
$YV = 2.25 + 2.25$
Add to solve:
$YV = 4.5$
