Question

A line containing the points (−2, 3)
(
−
2
,

3
)
and (2, 3)
(
2
,

3
)
is reflected across the x
x
-axis. How long is the reflected line?(1 point)
Responses

infinitely long
infinitely long

not enough information
not enough information

4 units
4 units

3 units
3 units

Answer 1

To determine the length of the original line segment connecting the points (-2, 3) and (2, 3), we can use the distance formula:

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

For the points (-2, 3) and (2, 3):

- \( x_1 = -2 \)
- \( y_1 = 3 \)
- \( x_2 = 2 \)
- \( y_2 = 3 \)

Plugging in these values:

\[
d = \sqrt{(2 - (-2))^2 + (3 - 3)^2} = \sqrt{(2 + 2)^2 + 0^2} = \sqrt{4^2} = \sqrt{16} = 4
\]

So, the length of the line segment is 4 units.

Now, when this line is reflected across the x-axis, the points will change as follows:
- The point (-2, 3) reflects to (-2, -3).
- The point (2, 3) reflects to (2, -3).

The reflected line segment now connects the points (-2, -3) and (2, -3), which forms the same horizontal distance (length) between the two points:

Calculating the distance between these points:

\[
d = \sqrt{(2 - (-2))^2 + (-3 - (-3))^2} = \sqrt{(2 + 2)^2 + 0^2} = \sqrt{4^2} = \sqrt{16} = 4
\]

The length of the reflected line segment is also 4 units.

So the answer is **4 units**.