Final answer:
To find the length of overline XY on a straight line, we calculate the length of overline XZ (which is 1/3 of overline YZ) and add it to the length of overline YZ, giving us a total length of 36 meters.
Step-by-step explanation:
The question given involves finding the length of overline XY on a straight line given that the length of overline XZ is 1/3 the length of overline YZ, and the length of overline YZ is 27 meters.
First, we can determine the length of overline XZ by dividing the length of overline YZ by 3:
overline XZ = overline YZ / 3
overline XZ = 27 m / 3
overline XZ = 9 m
Now, since point Z is between X and Y, the total length of overline XY is the sum of overline XZ and overline YZ:
overline XY = overline XZ + overline YZ
overline XY = 9 m + 27 m
overline XY = 36 m
Therefore, the length of overline XY is 36 meters.