Question

A line containing the points and is reflected across the -axis.
How long is the reflected line?(1 point)
(−2, 3) ( −2, 3 ) (2, 3) ( 2, 3 ) x𝑥
not enough information
infinitely long
3 units
4 units

Answer 1

To determine the length of the reflected line after reflecting the points across the x-axis, we first identify the original points that comprise the line.

The given points are:
1. \((-2, 3)\)
2. \((2, 3)\)

When these points are reflected across the x-axis, their y-coordinates change sign, resulting in:
1. \((-2, -3)\)
2. \((2, -3)\)

The reflected line consists of the points \((-2, -3)\) and \((2, -3)\).

Now, we can calculate the distance between these two points. The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:

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

Substituting our points into the formula:
- \((x_1, y_1) = (-2, -3)\)
- \((x_2, y_2) = (2, -3)\)

Now, substituting these 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 reflected line is **4 units**.