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

3 units
3 units

not enough information
not enough information

4 units
4 units

infinitely long

Answer 1

To determine the length of the line that is reflected across the x-axis, we first need to look at the original line defined by the points \((-2, 3)\) and \((2, 3)\).

1. **Find the length of the line segment**: The distance between the two points can be calculated using the distance formula:

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

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

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

Substituting the values into the formula:

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

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

2. **Reflect the line across the x-axis**: When the line is reflected across the x-axis, the y-coordinates of all points on the line will change signs, while the x-coordinates will stay the same. Therefore, the reflected points will be:

- The reflection of \((-2, 3)\) is \((-2, -3)\).
- The reflection of \((2, 3)\) is \((2, -3)\).

The reflected line segment now goes from \((-2, -3)\) to \((2, -3)\).

3. **Find the length of the reflected line segment**: Using the same distance formula as before for the points \((-2, -3)\) and \((2, -3)\):

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

Thus, the length of the reflected line is also 4 units.

The answer to the question is:

**4 units**.