A line containing the points (−2, 3) and (2, 3) is reflected across the x -axis. How long is the reflected line?

Question

1. not enough information
2. 3 units
3. infinitely long
4. 4 units

Answer 1

The line containing the points \((-2, 3)\) and \((2, 3)\) is a horizontal line, positioned at \(y = 3\).

When this line is reflected across the x-axis, the y-coordinates of every point on the line change sign. Therefore, the new points after reflection will be \((-2, -3)\) and \((2, -3)\).

To determine the length of the reflected line, we can find the distance between the two reflected points:

\[ \text{Distance} = |x_2 - x_1| = |2 - (-2)| = |2 + 2| = |4| = 4 \text{ units} \]

Thus, the length of the reflected line is \(4\) units.

The correct answer is:

4 units.