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)

1 unit

6 units

11 units

5 units

Answer 1

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

The original line segment has endpoints (0, 5) and (6, 5). The length of this line segment can be calculated using the distance formula:

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

In this case, \( (x_1, y_1) = (0, 5) \) and \( (x_2, y_2) = (6, 5) \):

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

After reflection across the x-axis, the new endpoints become (0, -5) and (6, -5). The distance between these new points remains the same:

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

Therefore, the length of the line segment after reflection remains **6 units**.

The answer is **6 units**.