## Geometry: Common Core (15th Edition)

If A is the midpoint of $\overline{XY}$, then $\overline{XA}=\overline{AY}$ (according to the definition of a midpoint). So, we can set up an equation using the values of $\overline{XA}$ and $\overline{AY}$ and setting them equal to each other. Our equation is $3x=5x-6$ Thus, we obtain: $$-2x=-6 \\ x=3$$ We now substitute 3 into the expressions. $XA=3x=3(3)=9$. $AY=5x-6=5(3)-6=15-6=9$ $XY=3x+5x-6=8x-6=8(3)-6=24-6=18$.