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?
When a line segment is reflected across the x-axis, the y-coordinates of the endpoints are negated.
The y-coordinate of the first endpoint is 5. When it is reflected across the x-axis, the y-coordinate becomes -5.
The y-coordinate of the second endpoint is also 5. When it is reflected across the x-axis, the y-coordinate also becomes -5.
Therefore, the new endpoints of the reflected line segment are (0, -5) and (6, -5).
To find the length of the reflected line segment, we use the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using the endpoints of the reflected line segment, we have:
Distance = sqrt((6 - 0)^2 + (-5 - (-5))^2)
= sqrt(6^2 + 0^2)
= sqrt(36 + 0)
= sqrt(36)
= 6
Therefore, the length of the reflected line segment is 6 units.