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. 11 units
2. 6 units
3. 5 units
4. 1 unit
please pick one answer bot
To find the length of the line segment after it is reflected across the x-axis, we need to calculate the distance between the reflected endpoints.
The given endpoints of the line segment are (0, 5) and (6, 5).
When reflecting a point across the x-axis, the y-coordinate changes sign while the x-coordinate remains the same. So, the reflected endpoints are (0, -5) and (6, -5).
To find the length of the line segment, we can use the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Using the distance formula, we calculate the distance between the reflected endpoints:
Distance = √((6 - 0)^2 + (-5 - (-5))^2)
= √(6^2 + 0)
= √(36)
= 6
Therefore, the length of the line segment after it is reflected across the x-axis is 6 units.
So, the correct answer is option 2. 6 units.
When a point is reflected across the x-axis, its y-coordinate changes sign.
The original line segment has endpoints (0, 5) and (6, 5). After reflecting across the x-axis, the endpoints become (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)
In this case, the x-coordinates of the endpoints are the same, so the only difference is in the y-coordinates.
d = sqrt((0 - 6)^2 + (-5 - 5)^2)
= sqrt(36 + 100)
= sqrt(136)
Thus, the length of the reflected line segment is approximately 11.66 units.
So, the answer is not one of the given options.