Final answer:
Since point R bisects XY, XR equals YR. By setting XR equal to YR and solving for n, we find that each segment is 18 units long, so the total length of XY is 36 units.
Step-by-step explanation:
When Point R bisects line segment XY, it means R divides XY into two equal parts. Given that XR is equal to 4n and YR is equal to 6n-9, we can set these two expressions equal to each other to find the value of n since XR should equal YR if R is truly the midpoint (bisector) of XY. So, 4n = 6n - 9. Solving for n, we subtract 4n from both sides to get 2n - 9 = 0, then add 9 to both sides to find that n = 4.5. Substituting n back into the expressions for XR and YR gives us XR = 4(4.5) = 18 and YR = 6(4.5) - 9 = 18. Therefore, the length of XY, which is the sum of XR and YR, is 18 + 18 = 36 units.