Answer
$\overline{YX} = 2.25$
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 $\overline{YX}$ is congruent to $\overline{WY}$, so they both have a length of $2.25$.
