A line containing the points (−2, 3)

Question

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

infinitely long
infinitely long

4 units
4 units

Answer 1

To determine the length of the reflected line, let's first analyze the original line containing the points \((-2, 3)\) and \((2, 3)\).

1. Find the length of the original line: Since both points have the same y-coordinate (3), the line is horizontal. The length can be calculated as the difference in the x-coordinates: \[ \text{Length} = |2 - (-2)| = |2 + 2| = |4| = 4 \text{ units} \]

2. Reflect the line across the x-axis: Reflecting the points across the x-axis means changing the sign of their y-coordinates.

   • The point \((-2, 3)\) becomes \((-2, -3)\)
   • The point \((2, 3)\) becomes \((2, -3)\)

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

3. Determine the length of the reflected line: The reflected line is also horizontal, with the same x-coordinates as before. The length remains the same: \[ \text{Length} = |2 - (-2)| = |2 + 2| = |4| = 4 \text{ units} \]

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

Therefore, the correct response is: 4 units.