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.
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