A line segment has endpoints (0, 5) and (6, 5) . After the line segment is reflected across the x -axis, how long will it be?(1 point)
When reflecting a line segment across the x-axis, the y-coordinates are reversed while the x-coordinates remain the same.
The original line segment has the y-coordinate of 5 for both endpoints, which remains unchanged when reflected. Therefore, the reflected line segment will have endpoints (0, -5) and (6, -5).
To find the length of the reflected line segment, we can use the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using the coordinates of the reflected endpoints, we can calculate the distance:
d = sqrt((6 - 0)^2 + (-5 - (-5))^2)
= sqrt(36 + 0)
= sqrt(36)
= 6
Therefore, the reflected line segment will have a length of 6 units.