Question

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

4 units
4 units

not enough information
not enough information

3 units
3 units

Answer 1

The points given, \((-2, 3)\) and \((2, 3)\), lie on a horizontal line at \(y = 3\). The length of the line segment between these two points can be calculated using the formula for distance between two points:

\[
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Here, \(x_1 = -2\), \(y_1 = 3\), \(x_2 = 2\), and \(y_2 = 3\).

Calculating the distance:

\[
\text{Distance} = \sqrt{(2 - (-2))^2 + (3 - 3)^2} = \sqrt{(2 + 2)^2 + 0^2} = \sqrt{4^2} = \sqrt{16} = 4
\]

Thus, the length of the line segment between those two points is 4 units.

When this line is reflected across the \(x\)-axis, the new coordinates of the reflecting points become \((-2, -3)\) and \((2, -3)\). However, the length of the line segment remains the same, because reflections do not change distances.

Therefore, the reflected line is also 4 units long.

So, the answer is **4 units**.