To find the length of the line segment after it is reflected across the x-axis, we first need to determine the coordinates of the endpoints after the reflection.
The original endpoints are (0, 5) and (6, 5). When reflected across the x-axis, the y-coordinates of the points change sign. Therefore, the new endpoints after reflection will be:
- (0, 5) becomes (0, -5)
- (6, 5) becomes (6, -5)
Now, we can calculate the length of the line segment between these new endpoints (0, -5) and (6, -5). The length of a line segment can be calculated using the distance formula:
\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Substituting in the coordinates of the new endpoints:
- \(x_1 = 0\), \(y_1 = -5\)
- \(x_2 = 6\), \(y_2 = -5\)
The distance calculation becomes:
\[ \text{Distance} = \sqrt{(6 - 0)^2 + (-5 - (-5))^2} \] \[ = \sqrt{(6)^2 + (0)^2} \] \[ = \sqrt{36 + 0} \] \[ = \sqrt{36} \] \[ = 6 \]
Thus, the length of the line segment after it is reflected across the x-axis will be 6 units.