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

11 units
11 units

1 unit
1 unit

6 units
6 units

5 units

Answer 1

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

The original endpoints are:
- (0, 5)
- (6, 5)

When reflecting across the x-axis, the y-coordinates of the points change sign. Therefore, the reflected endpoints will be:
- (0, -5)
- (6, -5)

Next, we use the distance formula to calculate the length of the line segment between these two points. The distance formula is:

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

Plugging in the coordinates of the reflected points:

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

Now, substituting these values into the formula:

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

Thus, the length of the line segment after the reflection across the x-axis remains 6 units.

The correct response is:
**6 units**.