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

5 units
5 units

11 units
11 units

1 unit
1 unit

6 units

Answer 1

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

The original line segment has endpoints at (0, 5) and (6, 5).

To find its length, we can use the distance formula between the two points:

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

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

Thus,

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

After reflecting across the x-axis, the new endpoints will be (0, -5) and (6, -5). The length of the line segment remains the same:

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

Therefore, after the reflection, the length will still be **6 units**.