1. **State the problem:** Find the length of segment $XY$ given that $X$ is the midpoint of segment $WY$, with $WX = 3x - 1$ and $WY = 10x - 26$. 2. **Recall the midpoint property:** The midpoint divides a segment into two equal parts, so: $$WX = XY = \frac{WY}{2}$$ 3. **Set up the equation:** Since $X$ is the midpoint, $$WX = XY$$ and $$WX + XY = WY$$ Therefore, $$2 \times WX = WY$$ Substitute the expressions: $$2(3x - 1) = 10x - 26$$ 4. **Solve for $x$:** $$6x - 2 = 10x - 26$$ Bring variables to one side: $$6x - 10x = -26 + 2$$ $$-4x = -24$$ Divide both sides by $-4$: $$x = 6$$ 5. **Find $XY$:** Since $XY = WX$, substitute $x=6$ into $WX$: $$WX = 3(6) - 1 = 18 - 1 = 17$$ **Final answer:** $$XY = 17$$