To find the length of the line segment defined by the points (-2, 3) and (2, 3), we first calculate the distance between these two points.
The length of the line segment can be calculated using the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
From the given points:
- Point 1: \((-2, 3)\)
- Point 2: \((2, 3)\)
Substituting these values into the distance formula:
\[ d = \sqrt{(2 - (-2))^2 + (3 - 3)^2} \] \[ d = \sqrt{(2 + 2)^2 + (0)^2} \] \[ d = \sqrt{(4)^2} \] \[ d = \sqrt{16} \] \[ d = 4 \]
Thus, the length of the line segment between these two points is 4 units.
When this line segment is reflected across the x-axis, the reflected points will change their y-coordinates to their opposites. The new points after reflection will be (-2, -3) and (2, -3), but the distance remains the same because the length of a line segment does not change with reflection.
Therefore, the length of the reflected line segment is still 4 units.
The correct response is 4 units.
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