Question

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

3 units
3 units

infinitely long
infinitely long

4 units
4 units

not enough information

Answer 1

When a line is reflected across the x-axis, the y-coordinates of all points on the line are negated, while the x-coordinates remain the same.

The original points given are \((-2, 3)\) and \((2, 3)\). This line is horizontal, as both points have the same y-coordinate.

After reflecting these points across the x-axis, the new points will be:
- The reflection of \((-2, 3)\) is \((-2, -3)\)
- The reflection of \((2, 3)\) is \((2, -3)\)

The reflected line still connects the points \((-2, -3)\) and \((2, -3)\), which is also a horizontal line.

To find the length of the reflected line, we can calculate the distance between the two points using the formula for the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

In our case, \(x_1 = -2\), \(y_1 = -3\), \(x_2 = 2\), and \(y_2 = -3\):
\[
\text{Distance} = \sqrt{(2 - (-2))^2 + (-3 - (-3))^2} = \sqrt{(2 + 2)^2 + (0)^2} = \sqrt{4^2} = \sqrt{16} = 4
\]

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

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