Question

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)
Responses

6 units
6 units

11 units
11 units

1 unit
1 unit

5 units

Answer 1

To find the length of the line segment after it is reflected across the x-axis, we first need to determine the coordinates of the endpoints after the reflection.

The original endpoints are (0, 5) and (6, 5). When reflected across the x-axis, the y-coordinates of the points change sign. Therefore, the new endpoints after reflection will be:

1. (0, 5) becomes (0, -5)
2. (6, 5) becomes (6, -5)

Now, we can calculate the length of the line segment between these new endpoints (0, -5) and (6, -5). The length of a line segment can be calculated using the distance formula:

\[
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Substituting in the coordinates of the new endpoints:

- \(x_1 = 0\), \(y_1 = -5\)
- \(x_2 = 6\), \(y_2 = -5\)

The distance calculation becomes:

\[
\text{Distance} = \sqrt{(6 - 0)^2 + (-5 - (-5))^2}
\]
\[
= \sqrt{(6)^2 + (0)^2}
\]
\[
= \sqrt{36 + 0}
\]
\[
= \sqrt{36}
\]
\[
= 6
\]

Thus, the length of the line segment after it is reflected across the x-axis will be **6 units**.