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)
The length of a line segment is determined by the difference between its endpoints. In this case, the line segment has the same y-coordinate for both endpoints, which means it is horizontal. Since the line segment is reflected across the x-axis, the y-coordinate will change sign. Therefore, the new endpoints of the reflected line segment will be (0, -5) and (6, -5), which are also horizontal and have the same y-coordinate.
The length of the reflected line segment is still determined by the difference between its endpoints, which is 6 units. Therefore, the length of the reflected line segment will still be 6 units.
To find the length of the line segment after it is reflected across the x-axis, we need to calculate the distance between the new endpoints of the reflected line.
Let's label the original endpoints as A(0, 5) and B(6, 5).
When the line segment is reflected across the x-axis, the y-coordinate of each point will change sign, while the x-coordinate remains the same.
So, the new endpoints will be A'(0, -5) and B'(6, -5).
To find the length of the reflected line segment, we will use the distance formula:
Distance = √((x2 - x1)² + (y2 - y1)²)
We can apply this formula to calculate the length:
Distance = √((6 - 0)² + (-5 - (-5))²)
The y-coordinates are the same for both endpoints, so the second term will be zero.
Distance = √((6 - 0)² + 0²)
Simplifying further:
Distance = √(6² + 0)
Distance = √(36)
Distance = 6
Therefore, the length of the line segment after being reflected across the x-axis is 6 units.