Reflecting the line segment across the x-axis will change the y-coordinates of the endpoints but not the x-coordinates.
The original endpoints of the line segment are (0, 5) and (6, 5). When reflected across the x-axis, these points become (0, -5) and (6, -5).
The length of the line segment can be calculated using the distance formula, which is given by:
\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
In this case, plug in the coordinates of the reflected points:
- \( (x_1, y_1) = (0, -5) \)
- \( (x_2, y_2) = (6, -5) \)
Calculating the distance:
\[ \text{Distance} = \sqrt{(6 - 0)^2 + (-5 - (-5))^2} = \sqrt{(6)^2 + (0)^2} = \sqrt{36} = 6 \]
Therefore, the length of the line segment after reflection across the x-axis remains 6 units.