To find the length of the line segment after it is reflected across the x-axis, we first determine the coordinates of the endpoints after reflection.
The original endpoints are:
- (0, 5)
- (6, 5)
When reflecting across the x-axis, the y-coordinates of the points change sign. Therefore, the reflected endpoints will be:
- (0, -5)
- (6, -5)
Next, we use the distance formula to calculate the length of the line segment between these two points. The distance formula is:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Plugging in the coordinates of the reflected points:
- \(x_1 = 0, y_1 = -5\)
- \(x_2 = 6, y_2 = -5\)
Now, substituting these values into the formula:
\[ d = \sqrt{(6 - 0)^2 + (-5 - (-5))^2} \] \[ d = \sqrt{(6)^2 + (0)^2} \] \[ d = \sqrt{36 + 0} \] \[ d = \sqrt{36} \] \[ d = 6 \]
Thus, the length of the line segment after the reflection across the x-axis remains 6 units.
The correct response is: 6 units.