Question

Transformations and Congruence Unit Test
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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

infinitely long
infinitely long

3 units
3 units

4 units
4 units

not enough information

Answer 1

To determine the length of the reflected line, we first need to examine the original line segment defined by the points \((-2, 3)\) and \((2, 3)\).

1. The distance between the two points can be calculated using the distance formula, which is given by:
\[
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

For our points:
- Point 1: \( (-2, 3) \)
- Point 2: \( (2, 3) \)

Plugging these into the distance formula:
\[
\text{Distance} = \sqrt{(2 - (-2))^2 + (3 - 3)^2} = \sqrt{(2 + 2)^2 + 0^2} = \sqrt{4^2} = \sqrt{16} = 4 \text{ units}
\]

2. Now, when we reflect the original line segment across the x-axis, the points transform as follows:
- The point \((-2, 3)\) reflects to \((-2, -3)\)
- The point \((2, 3)\) reflects to \((2, -3)\)

3. The reflected line segment is now defined by the points \((-2, -3)\) and \((2, -3)\). The distance between these two points is:
\[
\text{Distance} = \sqrt{(2 - (-2))^2 + (-3 - (-3))^2} = \sqrt{(2 + 2)^2 + 0^2} = \sqrt{4^2} = \sqrt{16} = 4 \text{ units}
\]

The length of the reflected line segment is still 4 units.

Therefore, the correct answer is:
**4 units**.