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

6 units
6 units

1 unit

Answer 1

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

The original line segment has endpoints (0, 5) and (6, 5). To find its length, we use the distance formula, which for two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

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

Calculating the length:

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

After reflecting across the x-axis, the new endpoints become \((0, -5)\) and \((6, -5)\).

Now, the length of the line segment between these new points will also be:

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

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

So the answer is:
**6 units**.