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. 1 unit
2. 11 units
3. 5 units
4. 6 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 new endpoints of the segment after reflection.

The endpoints of the line segment are (0, 5) and (6, 5). When we reflect a point (x, y) across the x-axis, the y-coordinate changes sign while the x-coordinate remains the same. Therefore, the reflections of the endpoints are as follows:

- The reflection of (0, 5) is (0, -5).
- The reflection of (6, 5) is (6, -5).

Now, we need to calculate the length of the line segment defined by the new endpoints (0, -5) and (6, -5). The length \( L \) of a line segment defined by two endpoints \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the distance formula:

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

Plugging in our endpoints \((0, -5)\) and \((6, -5)\):

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

Therefore, the length of the line segment after it is reflected across the x-axis remains **6 units**.

The answer is **4. 6 units**.