Math Snap

STEP 1

1. Points $X$, $Y$, and $Z$ are collinear.
2. The line segment $XZ$ includes the segments $XY$ and $YZ$.
3. The distances are measured in the same units.

STEP 2

1. Understand the relationship between the segments.
2. Use the segment addition postulate.
3. Solve for the unknown segment length.

STEP 3

Understand the relationship between the segments. Since $X$, $Y$, and $Z$ are collinear and in that order, the length of $XZ$ is the sum of the lengths of $XY$ and $YZ$.

STEP 4

Use the segment addition postulate, which states:
$$XZ = XY + YZ$$

Substitute the known values into the equation:
$$38 = XY + 11$$ Solve for $XY$:
$$XY = 38 - 11$$ $$XY = 27$$ The length of $\overline{XY}$ is:
$$\boxed{27}$$