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

not enough information
not enough information

4 units
4 units

infinitely long
infinitely long

3 units

Answer 1

To determine the length of the line after it is reflected across the x-axis, we first need to find the length of the line segment between the points \((-2, 3)\) and \((2, 3)\).

The formula for the length \(L\) of a line segment between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

Substituting in the coordinates of the points:

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

This means the length of the line segment between the points \((-2, 3)\) and \((2, 3)\) is \(4\) units.

Now, when we reflect this line across the x-axis, the y-coordinates of the points change sign, so the points transform as follows:
- The point \((-2, 3)\) becomes \((-2, -3)\).
- The point \((2, 3)\) becomes \((2, -3)\).

However, the length of the line segment does not change with reflection. Therefore, the length of the reflected line segment remains \(4\) units.

So the correct response is:

**4 units**