Question

A line containing the points (−2, 3)
and (2, 3)
is reflected across the 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

Answer 1

To find the length of the line segment defined by the points (-2, 3) and (2, 3), we first calculate the distance between these two points.

The length of the line segment can be calculated using the distance formula:

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

From the given points:
- Point 1: \((-2, 3)\)
- Point 2: \((2, 3)\)

Substituting these values into the distance formula:

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

Thus, the length of the line segment between these two points is 4 units.

When this line segment is reflected across the x-axis, the reflected points will change their y-coordinates to their opposites. The new points after reflection will be (-2, -3) and (2, -3), but the distance remains the same because the length of a line segment does not change with reflection.

Therefore, the length of the reflected line segment is still **4 units**.

The correct response is **4 units**.