Question

Question
A line segment has endpoints (0, 5)
(
0
,

5
)
and (6, 5)
(
6
,

5
)
. After the line segment is reflected across the x
𝑥
-axis, how long will it be?(1 point)
Responses

6 units
6 units

5 units
5 units

1 unit
1 unit

11 units

Answer 1

The length of a line segment is determined by the distance between its endpoints, regardless of the orientation of the segment.

The original endpoints of the line segment are (0, 5) and (6, 5). To find the length of the segment, we can use the distance formula, but in this simple case, we can see that since both y-coordinates are the same (5), the length of the segment is simply the difference between the x-coordinates:

Length = \(x_2 - x_1 = 6 - 0 = 6\) units.

Now, when this line segment is reflected across the x-axis, the y-coordinates of the endpoints change while the x-coordinates remain the same. The reflection of the endpoints will be (0, -5) and (6, -5).

However, the length of the segment remains the same, since length is not dependent on position, but rather the difference in coordinates. So, the length of the reflected segment is also:

Length = \(x_2 - x_1 = 6 - 0 = 6\) units.

Therefore, the answer is **6 units**.