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

5 units
5 units

6 units
6 units

Answer 1

The length of a line segment does not change when it is reflected across the x-axis.

To find the length of the original line segment with endpoints (0, 5) and (6, 5), you can use the distance formula:

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

For the endpoints (0, 5) and (6, 5):

\[
x_1 = 0, \quad y_1 = 5, \quad x_2 = 6, \quad y_2 = 5
\]

Plugging these values into the distance formula:

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

After reflection across the x-axis, the new endpoints will be (0, -5) and (6, -5), and the length will still be:

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

Thus, the length of the line segment after reflection is still **6 units**.