A line segment has endpoints (0, 5)

Question

and (6, 5)
. After the line segment is reflected across the x
-axis, how long will it be?(1 point)
Responses

6 units
6 units

11 units
11 units

1 unit
1 unit

5 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 coordinates of the endpoints after the reflection.

The original endpoints are (0, 5) and (6, 5). When reflected across the x-axis, the y-coordinates of the points change sign. Therefore, the new endpoints after reflection will be:

1. (0, 5) becomes (0, -5)
2. (6, 5) becomes (6, -5)

Now, we can calculate the length of the line segment between these new endpoints (0, -5) and (6, -5). The length of a line segment can be calculated using the distance formula:

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

Substituting in the coordinates of the new endpoints:

• $x_1=0$, $y_1=-5$
• $x_2=6$, $y_2=-5$

The distance calculation becomes:

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

Thus, the length of the line segment after it is reflected across the x-axis will be 6 units.