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

The line containing the points \((-2, 3)\) and \((2, 3)\) is a horizontal line at \(y = 3\). When this line is reflected across the x-axis, all the points on the line will change their y-coordinates to their negatives.

Thus, the points \((-2, 3)\) and \((2, 3)\) will be reflected to \((-2, -3)\) and \((2, -3)\), respectively. The new line will still be horizontal, but it will be at \(y = -3\).

To find the length of the reflected line segment between the two reflected points, we can calculate the distance between them:

The distance formula for two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
\text{Distance} = |x_2 - x_1|
\]

Substituting in our points:
\[
\text{Distance} = |2 - (-2)| = |2 + 2| = |4| = 4 \text{ units}
\]

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

The correct response is: **4 units**.