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, its y-coordinates change sign while its x-coordinates remain the same. So, the new endpoints of the reflected line segment would be (0,-5) and (6,-5).
To find the length of the reflected line segment, we can use the distance formula:
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Using the new endpoints, the distance becomes:
Distance = √((6 - 0)² + (-5 - 5)²)
= √(6² + (-10)²)
= √(36 + 100)
= √136
≈ 11.66
Therefore, the length of the reflected line segment is approximately 11.66 units.